diff --git a/src/function/arithmetic/norm.js b/src/function/arithmetic/norm.js
index 9ef2632b1f..7a86097d58 100644
--- a/src/function/arithmetic/norm.js
+++ b/src/function/arithmetic/norm.js
@@ -240,7 +240,7 @@ export const createNorm = /* #__PURE__ */ factory(
       const tx = ctranspose(x)
       const squaredX = multiply(tx, x)
       const eigenVals = eigs(squaredX).values
-      const rho = eigenVals.get([eigenVals.size()[0] - 1])
+      const rho = eigenVals[eigenVals.length - 1]
       return abs(sqrt(rho))
     }
 
diff --git a/src/function/complex/im.js b/src/function/complex/im.js
index d51fa29b77..b5e5faa465 100644
--- a/src/function/complex/im.js
+++ b/src/function/complex/im.js
@@ -41,6 +41,10 @@ export const createIm = /* #__PURE__ */ factory(name, dependencies, ({ typed })
       return x.mul(0)
     },
 
+    Fraction: function (x) {
+      return x.mul(0)
+    },
+
     Complex: function (x) {
       return x.im
     },
diff --git a/src/function/complex/re.js b/src/function/complex/re.js
index a22d1a68a1..3b98ecb108 100644
--- a/src/function/complex/re.js
+++ b/src/function/complex/re.js
@@ -41,6 +41,10 @@ export const createRe = /* #__PURE__ */ factory(name, dependencies, ({ typed })
       return x
     },
 
+    Fraction: function (x) {
+      return x
+    },
+
     Complex: function (x) {
       return x.re
     },
diff --git a/src/function/matrix/eigs.js b/src/function/matrix/eigs.js
index 36b85d6808..f061ee813a 100644
--- a/src/function/matrix/eigs.js
+++ b/src/function/matrix/eigs.js
@@ -1,373 +1,196 @@
-import { clone } from '../../utils/object.js'
 import { factory } from '../../utils/factory.js'
 import { format } from '../../utils/string.js'
+import { createComplex } from './eigs/complex.js'
+import { createRealSymmetric } from './eigs/realSymetric.js'
+import { typeOf, isNumber, isBigNumber, isComplex, isFraction } from '../../utils/is.js'
 
 const name = 'eigs'
-const dependencies = ['config', 'typed', 'matrix', 'addScalar', 'equal', 'subtract', 'abs', 'atan', 'cos', 'sin', 'multiplyScalar', 'inv', 'bignumber', 'multiply', 'add']
 
-export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ config, typed, matrix, addScalar, subtract, equal, abs, atan, cos, sin, multiplyScalar, inv, bignumber, multiply, add }) => {
+// The absolute state of math.js's dependency system:
+const dependencies = ['config', 'typed', 'matrix', 'addScalar', 'equal', 'subtract', 'abs', 'atan', 'cos', 'sin', 'multiplyScalar', 'divideScalar', 'inv', 'bignumber', 'multiply', 'add', 'larger', 'column', 'flatten', 'number', 'complex', 'sqrt', 'diag', 'qr', 'usolveAll', 'im', 're', 'smaller', 'round', 'log10', 'transpose']
+export const createEigs = /* #__PURE__ */ factory(name, dependencies, ({ config, typed, matrix, addScalar, subtract, equal, abs, atan, cos, sin, multiplyScalar, divideScalar, inv, bignumber, multiply, add, larger, column, flatten, number, complex, sqrt, diag, qr, usolveAll, im, re, smaller, round, log10, transpose }) => {
+  const doRealSymetric = createRealSymmetric({ config, addScalar, subtract, column, flatten, equal, abs, atan, cos, sin, multiplyScalar, inv, bignumber, complex, multiply, add })
+  const doComplex = createComplex({ config, addScalar, subtract, multiply, multiplyScalar, flatten, divideScalar, sqrt, abs, bignumber, diag, qr, inv, usolveAll, equal, complex, larger, smaller, round, log10, transpose })
+
   /**
-   * Compute eigenvalue and eigenvector of a real symmetric matrix.
-   * Only applicable to two dimensional symmetric matrices. Uses Jacobi
-   * Algorithm. Matrix containing mixed type ('number', 'bignumber', 'fraction')
-   * of elements are not supported. Input matrix or 2D array should contain all elements
-   * of either 'number', 'bignumber' or 'fraction' type. For 'number' and 'fraction', the
-   * eigenvalues are of 'number' type. For 'bignumber' the eigenvalues are of ''bignumber' type.
-   * Eigenvectors are always of 'number' type.
+   * Compute eigenvalues and eigenvectors of a matrix. The eigenvalues are sorted by their absolute value, ascending.
+   * An eigenvalue with multiplicity k will be listed k times. The eigenvectors are returned as columns of a matrix –
+   * the eigenvector that belongs to the j-th eigenvalue in the list (eg. `values[j]`) is the j-th column (eg. `column(vectors, j)`).
+   * If the algorithm fails to converge, it will throw an error – in that case, however, you may still find useful information
+   * in `err.values` and `err.vectors`.
    *
    * Syntax:
    *
-   *     math.eigs(x)
+   *     math.eigs(x, [prec])
    *
    * Examples:
    *
+   *     const { eigs, multiply, column, transpose } = math
    *     const H = [[5, 2.3], [2.3, 1]]
-   *     const ans = math.eigs(H) // returns {values: [E1,E2...sorted], vectors: [v1,v2.... corresponding vectors as columns]}
+   *     const ans = eigs(H) // returns {values: [E1,E2...sorted], vectors: [v1,v2.... corresponding vectors as columns]}
    *     const E = ans.values
    *     const U = ans.vectors
-   *     math.multiply(H, math.column(U, 0)) // returns math.multiply(E[0], math.column(U, 0))
-   *     const UTxHxU = math.multiply(math.transpose(U), H, U) // rotates H to the eigen-representation
+   *     multiply(H, column(U, 0)) // returns multiply(E[0], column(U, 0))
+   *     const UTxHxU = multiply(transpose(U), H, U) // diagonalizes H
    *     E[0] == UTxHxU[0][0]  // returns true
+   *
    * See also:
    *
    *     inv
    *
    * @param {Array | Matrix} x  Matrix to be diagonalized
-   * @return {{values: Array, vectors: Array} | {values: Matrix, vectors: Matrix}} Object containing eigenvalues (Array or Matrix) and eigenvectors (2D Array/Matrix with eigenvectors as columns).
+   *
+   * @param {number | BigNumber} [prec] Precision, default value: 1e-15
+   * @return {{values: Array, vectors: Matrix}} Object containing an array of eigenvalues and a matrix with eigenvectors as columns.
+   *
    */
   return typed('eigs', {
 
     Array: function (x) {
-      // check array size
       const mat = matrix(x)
-      const size = mat.size()
-      if (size.length !== 2 || size[0] !== size[1]) {
-        throw new RangeError('Matrix must be square ' +
-          '(size: ' + format(size) + ')')
-      }
+      return computeValuesAndVectors(mat)
+    },
 
-      // use dense 2D matrix implementation
-      const ans = checkAndSubmit(mat, size[0])
-      return { values: ans[0], vectors: ans[1] }
+    'Array, number|BigNumber': function (x, prec) {
+      const mat = matrix(x)
+      return computeValuesAndVectors(mat, prec)
     },
 
-    Matrix: function (x) {
-      // use dense 2D array implementation
-      // dense matrix
-      const size = x.size()
-      if (size.length !== 2 || size[0] !== size[1]) {
-        throw new RangeError('Matrix must be square ' +
-          '(size: ' + format(size) + ')')
-      }
-      const ans = checkAndSubmit(x, size[0])
-      return { values: matrix(ans[0]), vectors: matrix(ans[1]) }
+    Matrix: function (mat) {
+      return computeValuesAndVectors(mat)
+    },
+
+    'Matrix, number|BigNumber': function (mat, prec) {
+      return computeValuesAndVectors(mat, prec)
     }
   })
 
-  // Is the matrix
-  // symmetric ?
-  function isSymmetric (x, n) {
-    for (let i = 0; i < n; i++) {
-      for (let j = i; j < n; j++) {
-        // not symmtric
-        if (!equal(x[i][j], x[j][i])) {
-          throw new TypeError('Input matrix is not symmetric')
-        }
-      }
+  function computeValuesAndVectors (mat, prec) {
+    if (prec === undefined) {
+      prec = config.epsilon
     }
-  }
 
-  // check input for possible problems
-  // and perform diagonalization efficiently for
-  // specific type of number
-  function checkAndSubmit (x, n) {
-    let type = x.datatype()
-    // type check
-    if (type === undefined) {
-      type = x.getDataType()
+    const size = mat.size()
+
+    if (size.length !== 2 || size[0] !== size[1]) {
+      throw new RangeError('Matrix must be square (size: ' + format(size) + ')')
     }
-    if (type !== 'number' && type !== 'BigNumber' && type !== 'Fraction') {
-      if (type === 'mixed') {
-        throw new TypeError('Mixed matrix element type is not supported')
-      } else {
-        throw new TypeError('Matrix element type not supported (' + type + ')')
+
+    const arr = mat.toArray()
+    const N = size[0]
+
+    if (isReal(arr, N, prec)) {
+      coerceReal(arr, N)
+
+      if (isSymmetric(arr, N, prec)) {
+        const type = coerceTypes(mat, arr, N)
+        return doRealSymetric(arr, N, prec, type)
       }
-    } else {
-      isSymmetric(x.toArray(), n)
     }
 
-    // perform efficient calculation for 'numbers'
-    if (type === 'number') {
-      return diag(x.toArray())
-    } else if (type === 'Fraction') {
-      const xArr = x.toArray()
-      // convert fraction to numbers
-      for (let i = 0; i < n; i++) {
-        for (let j = i; j < n; j++) {
-          xArr[i][j] = xArr[i][j].valueOf()
-          xArr[j][i] = xArr[i][j]
+    const type = coerceTypes(mat, arr, N)
+    return doComplex(arr, N, prec, type)
+  }
+
+  /** @return {boolean} */
+  function isSymmetric (arr, N, prec) {
+    for (let i = 0; i < N; i++) {
+      for (let j = i; j < N; j++) {
+        // TODO proper comparison of bignum and frac
+        if (larger(bignumber(abs(subtract(arr[i][j], arr[j][i]))), prec)) {
+          return false
         }
       }
-      return diag(x.toArray())
-    } else if (type === 'BigNumber') {
-      return diagBig(x.toArray())
     }
+
+    return true
   }
 
-  // diagonalization implementation for number (efficient)
-  function diag (x) {
-    const N = x.length
-    const e0 = Math.abs(config.epsilon / N)
-    let psi
-    let Sij = new Array(N)
-    // Sij is Identity Matrix
-    for (let i = 0; i < N; i++) {
-      Sij[i] = createArray(N, 0)
-      Sij[i][i] = 1.0
-    }
-    // initial error
-    let Vab = getAij(x)
-    while (Math.abs(Vab[1]) >= Math.abs(e0)) {
-      const i = Vab[0][0]
-      const j = Vab[0][1]
-      psi = getTheta(x[i][i], x[j][j], x[i][j])
-      x = x1(x, psi, i, j)
-      Sij = Sij1(Sij, psi, i, j)
-      Vab = getAij(x)
-    }
-    const Ei = createArray(N, 0) // eigenvalues
+  /** @return {boolean} */
+  function isReal (arr, N, prec) {
     for (let i = 0; i < N; i++) {
-      Ei[i] = x[i][i]
+      for (let j = 0; j < N; j++) {
+        // TODO proper comparison of bignum and frac
+        if (larger(bignumber(abs(im(arr[i][j]))), prec)) {
+          return false
+        }
+      }
     }
-    return sorting(clone(Ei), clone(Sij))
+
+    return true
   }
 
-  // diagonalization implementation for bigNumber
-  function diagBig (x) {
-    const N = x.length
-    const e0 = abs(config.epsilon / N)
-    let psi
-    let Sij = new Array(N)
-    // Sij is Identity Matrix
-    for (let i = 0; i < N; i++) {
-      Sij[i] = createArray(N, 0)
-      Sij[i][i] = 1.0
-    }
-    // initial error
-    let Vab = getAijBig(x)
-    while (abs(Vab[1]) >= abs(e0)) {
-      const i = Vab[0][0]
-      const j = Vab[0][1]
-      psi = getThetaBig(x[i][i], x[j][j], x[i][j])
-      x = x1Big(x, psi, i, j)
-      Sij = Sij1Big(Sij, psi, i, j)
-      Vab = getAijBig(x)
-    }
-    const Ei = createArray(N, 0) // eigenvalues
+  function coerceReal (arr, N) {
     for (let i = 0; i < N; i++) {
-      Ei[i] = x[i][i]
+      for (let j = 0; j < N; j++) {
+        arr[i][j] = re(arr[i][j])
+      }
     }
-    // return [clone(Ei), clone(Sij)]
-    return sorting(clone(Ei), clone(Sij))
   }
 
-  // get angle
-  function getTheta (aii, ajj, aij) {
-    const denom = (ajj - aii)
-    if (Math.abs(denom) <= config.epsilon) {
-      return Math.PI / 4
-    } else {
-      return 0.5 * Math.atan(2 * aij / (ajj - aii))
-    }
-  }
+  /** @return {'number' | 'BigNumber' | 'Complex'} */
+  function coerceTypes (mat, arr, N) {
+    /** @type {string} */
+    const type = mat.datatype()
 
-  // get angle
-  function getThetaBig (aii, ajj, aij) {
-    const denom = subtract(ajj, aii)
-    if (abs(denom) <= config.epsilon) {
-      return bignumber(-1).acos().div(4)
-    } else {
-      return multiplyScalar(0.5, atan(multiply(2, aij, inv(denom))))
+    if (type === 'number' || type === 'BigNumber' || type === 'Complex') {
+      return type
     }
-  }
 
-  // update eigvec
-  function Sij1 (Sij, theta, i, j) {
-    const N = Sij.length
-    const c = Math.cos(theta)
-    const s = Math.sin(theta)
-    const Ski = createArray(N, 0)
-    const Skj = createArray(N, 0)
-    for (let k = 0; k < N; k++) {
-      Ski[k] = c * Sij[k][i] - s * Sij[k][j]
-      Skj[k] = s * Sij[k][i] + c * Sij[k][j]
-    }
-    for (let k = 0; k < N; k++) {
-      Sij[k][i] = Ski[k]
-      Sij[k][j] = Skj[k]
-    }
-    return Sij
-  }
-  // update eigvec for overlap
-  function Sij1Big (Sij, theta, i, j) {
-    const N = Sij.length
-    const c = cos(theta)
-    const s = sin(theta)
-    const Ski = createArray(N, bignumber(0))
-    const Skj = createArray(N, bignumber(0))
-    for (let k = 0; k < N; k++) {
-      Ski[k] = subtract(multiplyScalar(c, Sij[k][i]), multiplyScalar(s, Sij[k][j]))
-      Skj[k] = addScalar(multiplyScalar(s, Sij[k][i]), multiplyScalar(c, Sij[k][j]))
-    }
-    for (let k = 0; k < N; k++) {
-      Sij[k][i] = Ski[k]
-      Sij[k][j] = Skj[k]
-    }
-    return Sij
-  }
+    let hasNumber = false
+    let hasBig = false
+    let hasComplex = false
 
-  // update matrix
-  function x1Big (Hij, theta, i, j) {
-    const N = Hij.length
-    const c = bignumber(cos(theta))
-    const s = bignumber(sin(theta))
-    const c2 = multiplyScalar(c, c)
-    const s2 = multiplyScalar(s, s)
-    const Aki = createArray(N, bignumber(0))
-    const Akj = createArray(N, bignumber(0))
-    // 2cs Hij
-    const csHij = multiply(bignumber(2), c, s, Hij[i][j])
-    //  Aii
-    const Aii = addScalar(subtract(multiplyScalar(c2, Hij[i][i]), csHij), multiplyScalar(s2, Hij[j][j]))
-    const Ajj = add(multiplyScalar(s2, Hij[i][i]), csHij, multiplyScalar(c2, Hij[j][j]))
-    // 0  to i
-    for (let k = 0; k < N; k++) {
-      Aki[k] = subtract(multiplyScalar(c, Hij[i][k]), multiplyScalar(s, Hij[j][k]))
-      Akj[k] = addScalar(multiplyScalar(s, Hij[i][k]), multiplyScalar(c, Hij[j][k]))
-    }
-    // Modify Hij
-    Hij[i][i] = Aii
-    Hij[j][j] = Ajj
-    Hij[i][j] = bignumber(0)
-    Hij[j][i] = bignumber(0)
-    // 0  to i
-    for (let k = 0; k < N; k++) {
-      if (k !== i && k !== j) {
-        Hij[i][k] = Aki[k]
-        Hij[k][i] = Aki[k]
-        Hij[j][k] = Akj[k]
-        Hij[k][j] = Akj[k]
+    for (let i = 0; i < N; i++) {
+      for (let j = 0; j < N; j++) {
+        const el = arr[i][j]
+
+        if (isNumber(el) || isFraction(el)) {
+          hasNumber = true
+        } else if (isBigNumber(el)) {
+          hasBig = true
+        } else if (isComplex(el)) {
+          hasComplex = true
+        } else {
+          throw TypeError('Unsupported type in Matrix: ' + typeOf(el))
+        }
       }
     }
-    return Hij
-  }
 
-  // update matrix
-  function x1 (Hij, theta, i, j) {
-    const N = Hij.length
-    const c = Math.cos(theta)
-    const s = Math.sin(theta)
-    const c2 = c * c
-    const s2 = s * s
-    const Aki = createArray(N, 0)
-    const Akj = createArray(N, 0)
-    //  Aii
-    const Aii = c2 * Hij[i][i] - 2 * c * s * Hij[i][j] + s2 * Hij[j][j]
-    const Ajj = s2 * Hij[i][i] + 2 * c * s * Hij[i][j] + c2 * Hij[j][j]
-    // 0  to i
-    for (let k = 0; k < N; k++) {
-      Aki[k] = c * Hij[i][k] - s * Hij[j][k]
-      Akj[k] = s * Hij[i][k] + c * Hij[j][k]
-    }
-    // Modify Hij
-    Hij[i][i] = Aii
-    Hij[j][j] = Ajj
-    Hij[i][j] = 0
-    Hij[j][i] = 0
-    // 0  to i
-    for (let k = 0; k < N; k++) {
-      if (k !== i && k !== j) {
-        Hij[i][k] = Aki[k]
-        Hij[k][i] = Aki[k]
-        Hij[j][k] = Akj[k]
-        Hij[k][j] = Akj[k]
-      }
+    if (hasBig && hasComplex) {
+      console.warn('Complex BigNumbers not supported, this operation will lose precission.')
     }
-    return Hij
-  }
 
-  // get max off-diagonal value from Upper Diagonal
-  function getAij (Mij) {
-    const N = Mij.length
-    let maxMij = 0
-    let maxIJ = [0, 1]
-    for (let i = 0; i < N; i++) {
-      for (let j = i + 1; j < N; j++) {
-        if (Math.abs(maxMij) < Math.abs(Mij[i][j])) {
-          maxMij = Math.abs(Mij[i][j])
-          maxIJ = [i, j]
+    if (hasComplex) {
+      for (let i = 0; i < N; i++) {
+        for (let j = 0; j < N; j++) {
+          arr[i][j] = complex(arr[i][j])
         }
       }
+
+      return 'Complex'
     }
-    return [maxIJ, maxMij]
-  }
 
-  // get max off-diagonal value from Upper Diagonal
-  function getAijBig (Mij) {
-    const N = Mij.length
-    let maxMij = 0
-    let maxIJ = [0, 1]
-    for (let i = 0; i < N; i++) {
-      for (let j = i + 1; j < N; j++) {
-        if (abs(maxMij) < abs(Mij[i][j])) {
-          maxMij = abs(Mij[i][j])
-          maxIJ = [i, j]
+    if (hasBig) {
+      for (let i = 0; i < N; i++) {
+        for (let j = 0; j < N; j++) {
+          arr[i][j] = bignumber(arr[i][j])
         }
       }
-    }
-    return [maxIJ, maxMij]
-  }
 
-  // sort results
-  function sorting (E, S) {
-    const N = E.length
-    const Ef = Array(N)
-    const Sf = Array(N)
-    for (let k = 0; k < N; k++) {
-      Sf[k] = Array(N)
+      return 'BigNumber'
     }
-    for (let i = 0; i < N; i++) {
-      let minID = 0
-      let minE = E[0]
-      for (let j = 0; j < E.length; j++) {
-        if (E[j] < minE) {
-          minID = j
-          minE = E[minID]
+
+    if (hasNumber) {
+      for (let i = 0; i < N; i++) {
+        for (let j = 0; j < N; j++) {
+          arr[i][j] = number(arr[i][j])
         }
       }
-      Ef[i] = E.splice(minID, 1)[0]
-      for (let k = 0; k < N; k++) {
-        Sf[k][i] = S[k][minID]
-        S[k].splice(minID, 1)
-      }
-    }
-    return [clone(Ef), clone(Sf)]
-  }
-
-  /**
-   * Create an array of a certain size and fill all items with an initial value
-   * @param {number} size
-   * @param {number} value
-   * @return {number[]}
-   */
-  function createArray (size, value) {
-    // TODO: as soon as all browsers support Array.fill, use that instead (IE doesn't support it)
-    const array = new Array(size)
 
-    for (let i = 0; i < size; i++) {
-      array[i] = value
+      return 'number'
+    } else {
+      throw TypeError('Matrix contains unsupported types only.')
     }
-
-    return array
   }
 })
diff --git a/src/function/matrix/eigs/complex.js b/src/function/matrix/eigs/complex.js
new file mode 100644
index 0000000000..c1eb9c5c02
--- /dev/null
+++ b/src/function/matrix/eigs/complex.js
@@ -0,0 +1,576 @@
+import { clone } from '../../../utils/object.js'
+
+export function createComplex ({ addScalar, subtract, flatten, multiply, multiplyScalar, divideScalar, sqrt, abs, bignumber, diag, inv, qr, usolveAll, equal, complex, larger, smaller, round, log10, transpose }) {
+  /**
+   * @param {number[][]} arr the matrix to find eigenvalues of
+   * @param {number} N size of the matrix
+   * @param {number|BigNumber} prec precision, anything lower will be considered zero
+   * @param {'number'|'BigNumber'|'Complex'} type
+   * @param {boolean} findVectors should we find eigenvectors?
+   */
+  function main (arr, N, prec, type, findVectors) {
+    if (findVectors === undefined) {
+      findVectors = true
+    }
+
+    // TODO check if any row/col are zero except the diagonal
+
+    // make sure corresponding rows and columns have similar magnitude
+    // important because of numerical stability
+    const R = balance(arr, N, prec, type, findVectors)
+
+    // R is the row transformation matrix
+    // A' = R A R⁻¹, A is the original matrix
+    // (if findVectors is false, R is undefined)
+
+    // TODO if magnitudes of elements vary over many orders,
+    // move greatest elements to the top left corner
+
+    // using similarity transformations, reduce the matrix
+    // to Hessenberg form (upper triangular plus one subdiagonal row)
+    // updates the transformation matrix R with new row operationsq
+    reduceToHessenberg(arr, N, prec, type, findVectors, R)
+
+    // find eigenvalues
+    let { values, C } = iterateUntilTriangular(arr, N, prec, type, findVectors)
+
+    // values is the list of eigenvalues, C is the column
+    // transformation matrix that transforms the hessenberg
+    // matrix to upper triangular
+
+    // compose transformations A → hess. and hess. → triang.
+    C = multiply(inv(R), C)
+
+    let vectors
+
+    if (findVectors) {
+      vectors = findEigenvectors(arr, N, C, values, prec)
+      vectors = transpose((vectors)) // vectors are columns of a matrix
+    }
+
+    return { values, vectors }
+  }
+
+  /**
+   * @param {number[][]} arr
+   * @param {number} N
+   * @param {number} prec
+   * @param {'number'|'BigNumber'|'Complex'} type
+   * @returns {number[][]}
+   */
+  function balance (arr, N, prec, type, findVectors) {
+    const big = type === 'BigNumber'
+    const cplx = type === 'Complex'
+
+    const zero = big ? bignumber(0) : cplx ? complex(0) : 0
+    const one = big ? bignumber(1) : cplx ? complex(1) : 1
+
+    // base of the floating-point arithmetic
+    const radix = big ? bignumber(10) : 2
+    const radixSq = multiplyScalar(radix, radix)
+
+    // the diagonal transformation matrix R
+    let Rdiag
+    if (findVectors) {
+      Rdiag = Array(N).fill(one)
+    }
+
+    // this isn't the only time we loop thru the matrix...
+    let last = false
+
+    while (!last) {
+      // ...haha I'm joking! unless...
+      last = true
+
+      for (let i = 0; i < N; i++) {
+        // compute the taxicab norm of i-th column and row
+        // TODO optimize for complex numbers
+        let colNorm = zero
+        let rowNorm = zero
+
+        for (let j = 0; j < N; j++) {
+          if (i === j) continue
+          const c = abs(arr[i][j])
+          colNorm = addScalar(colNorm, c)
+          rowNorm = addScalar(rowNorm, c)
+        }
+
+        if (!equal(colNorm, 0) && !equal(rowNorm, 0)) {
+          // find integer power closest to balancing the matrix
+          // (we want to scale only by integer powers of radix,
+          // so that we don't lose any precision due to round-off)
+
+          let f = one
+          let c = colNorm
+
+          const rowDivRadix = divideScalar(rowNorm, radix)
+          const rowMulRadix = multiplyScalar(rowNorm, radix)
+
+          while (smaller(c, rowDivRadix)) {
+            c = multiplyScalar(c, radixSq)
+            f = multiplyScalar(f, radix)
+          }
+          while (larger(c, rowMulRadix)) {
+            c = divideScalar(c, radixSq)
+            f = divideScalar(f, radix)
+          }
+
+          // check whether balancing is needed
+          // condition = (c + rowNorm) / f < 0.95 * (colNorm + rowNorm)
+          const condition = smaller(divideScalar(addScalar(c, rowNorm), f), multiplyScalar(addScalar(colNorm, rowNorm), 0.95))
+
+          // apply balancing similarity transformation
+          if (condition) {
+            // we should loop once again to check whether
+            // another rebalancing is needed
+            last = false
+
+            const g = divideScalar(1, f)
+
+            for (let j = 0; j < N; j++) {
+              if (i === j) {
+                continue
+              }
+              arr[i][j] = multiplyScalar(arr[i][j], f)
+              arr[j][i] = multiplyScalar(arr[j][i], g)
+            }
+
+            // keep track of transformations
+            if (findVectors) {
+              Rdiag[i] = multiplyScalar(Rdiag[i], f)
+            }
+          }
+        }
+      }
+    }
+
+    // return the diagonal row transformation matrix
+    return diag(Rdiag)
+  }
+
+  /**
+   * @param {number[][]} arr
+   * @param {number} N
+   * @param {number} prec
+   * @param {'number'|'BigNumber'|'Complex'} type
+   * @param {boolean} findVectors
+   * @param {number[][]} R the row transformation matrix that will be modified
+   */
+  function reduceToHessenberg (arr, N, prec, type, findVectors, R) {
+    const big = type === 'BigNumber'
+    const cplx = type === 'Complex'
+
+    const zero = big ? bignumber(0) : cplx ? complex(0) : 0
+
+    if (big) { prec = bignumber(prec) }
+
+    for (let i = 0; i < N - 2; i++) {
+      // Find the largest subdiag element in the i-th col
+
+      let maxIndex = 0
+      let max = zero
+
+      for (let j = i + 1; j < N; j++) {
+        const el = arr[j][i]
+        if (smaller(abs(max), abs(el))) {
+          max = el
+          maxIndex = j
+        }
+      }
+
+      // This col is pivoted, no need to do anything
+      if (smaller(abs(max), prec)) {
+        continue
+      }
+
+      if (maxIndex !== i + 1) {
+        // Interchange maxIndex-th and (i+1)-th row
+        const tmp1 = arr[maxIndex]
+        arr[maxIndex] = arr[i + 1]
+        arr[i + 1] = tmp1
+
+        // Interchange maxIndex-th and (i+1)-th column
+        for (let j = 0; j < N; j++) {
+          const tmp2 = arr[j][maxIndex]
+          arr[j][maxIndex] = arr[j][i + 1]
+          arr[j][i + 1] = tmp2
+        }
+
+        // keep track of transformations
+        if (findVectors) {
+          const tmp3 = R[maxIndex]
+          R[maxIndex] = R[i + 1]
+          R[i + 1] = tmp3
+        }
+      }
+
+      // Reduce following rows and columns
+      for (let j = i + 2; j < N; j++) {
+        const n = divideScalar(arr[j][i], max)
+
+        if (n === 0) {
+          continue
+        }
+
+        // from j-th row subtract n-times (i+1)th row
+        for (let k = 0; k < N; k++) {
+          arr[j][k] = subtract(arr[j][k], multiplyScalar(n, arr[i + 1][k]))
+        }
+
+        // to (i+1)th column add n-times j-th column
+        for (let k = 0; k < N; k++) {
+          arr[k][i + 1] = addScalar(arr[k][i + 1], multiplyScalar(n, arr[k][j]))
+        }
+
+        // keep track of transformations
+        if (findVectors) {
+          for (let k = 0; k < N; k++) {
+            R[j][k] = subtract(R[j][k], multiplyScalar(n, R[i + 1][k]))
+          }
+        }
+      }
+    }
+
+    return R
+  }
+
+  /**
+   * @returns {{values: values, C: Matrix}}
+   * @see Press, Wiliams: Numerical recipes in Fortran 77
+   * @see https://en.wikipedia.org/wiki/QR_algorithm
+   */
+  function iterateUntilTriangular (A, N, prec, type, findVectors) {
+    const big = type === 'BigNumber'
+    const cplx = type === 'Complex'
+
+    const one = big ? bignumber(1) : cplx ? complex(1) : 1
+
+    if (big) { prec = bignumber(prec) }
+
+    // The Francis Algorithm
+    // The core idea of this algorithm is that doing successive
+    // A' = Q⁺AQ transformations will eventually converge to block-
+    // upper-triangular with diagonal blocks either 1x1 or 2x2.
+    // The Q here is the one from the QR decomposition, A = QR.
+    // Since the eigenvalues of a block-upper-triangular matrix are
+    // the eigenvalues of its diagonal blocks and we know how to find
+    // eigenvalues of a 2x2 matrix, we know the eigenvalues of A.
+
+    let arr = clone(A)
+
+    // the list of converged eigenvalues
+    const lambdas = []
+
+    // size of arr, which will get smaller as eigenvalues converge
+    let n = N
+
+    // the diagonal of the block-diagonal matrix that turns
+    // converged 2x2 matrices into upper triangular matrices
+    const Sdiag = []
+
+    // N×N matrix describing the overall transformation done during the QR algorithm
+    let Qtotal = findVectors ? diag(Array(N).fill(one)) : undefined
+
+    // n×n matrix describing the QR transformations done since last convergence
+    let Qpartial = findVectors ? diag(Array(n).fill(one)) : undefined
+
+    // last eigenvalue converged before this many steps
+    let lastConvergenceBefore = 0
+
+    while (lastConvergenceBefore <= 100) {
+      lastConvergenceBefore += 1
+
+      // TODO if the convergence is slow, do something clever
+
+      // Perform the factorization
+
+      const k = 0 // TODO set close to an eigenvalue
+
+      for (let i = 0; i < n; i++) {
+        arr[i][i] = subtract(arr[i][i], k)
+      }
+
+      // TODO do an implicit QR transformation
+      const { Q, R } = qr(arr)
+      arr = multiply(R, Q)
+
+      for (let i = 0; i < n; i++) {
+        arr[i][i] = addScalar(arr[i][i], k)
+      }
+
+      // keep track of transformations
+      if (findVectors) {
+        Qpartial = multiply(Qpartial, Q)
+      }
+
+      // The rightmost diagonal element converged to an eigenvalue
+      if (n === 1 || smaller(abs(arr[n - 1][n - 2]), prec)) {
+        lastConvergenceBefore = 0
+        lambdas.push(arr[n - 1][n - 1])
+
+        // keep track of transformations
+        if (findVectors) {
+          Sdiag.unshift([[1]])
+          inflateMatrix(Qpartial, N)
+          Qtotal = multiply(Qtotal, Qpartial)
+
+          if (n > 1) {
+            Qpartial = diag(Array(n - 1).fill(one))
+          }
+        }
+
+        // reduce the matrix size
+        n -= 1
+        arr.pop()
+        for (let i = 0; i < n; i++) {
+          arr[i].pop()
+        }
+
+      // The rightmost diagonal 2x2 block converged
+      } else if (n === 2 || smaller(abs(arr[n - 2][n - 3]), prec)) {
+        lastConvergenceBefore = 0
+        const ll = eigenvalues2x2(
+          arr[n - 2][n - 2], arr[n - 2][n - 1],
+          arr[n - 1][n - 2], arr[n - 1][n - 1]
+        )
+        lambdas.push(...ll)
+
+        // keep track of transformations
+        if (findVectors) {
+          Sdiag.unshift(jordanBase2x2(
+            arr[n - 2][n - 2], arr[n - 2][n - 1],
+            arr[n - 1][n - 2], arr[n - 1][n - 1],
+            ll[0], ll[1], prec, type
+          ))
+          inflateMatrix(Qpartial, N)
+          Qtotal = multiply(Qtotal, Qpartial)
+
+          if (n > 2) {
+            Qpartial = diag(Array(n - 2).fill(one))
+          }
+        }
+
+        // reduce the matrix size
+        n -= 2
+        arr.pop()
+        arr.pop()
+        for (let i = 0; i < n; i++) {
+          arr[i].pop()
+          arr[i].pop()
+        }
+      }
+
+      if (n === 0) {
+        break
+      }
+    }
+
+    // standard sorting
+    lambdas.sort((a, b) => +subtract(abs(a), abs(b)))
+
+    // the algorithm didn't converge
+    if (lastConvergenceBefore > 100) {
+      const err = Error('The eigenvalues failed to converge. Only found these eigenvalues: ' + lambdas.join(', '))
+      err.values = lambdas
+      err.vectors = []
+      throw err
+    }
+
+    // combine the overall QR transformation Qtotal with the subsequent
+    // transformation S that turns the diagonal 2x2 blocks to upper triangular
+    const C = findVectors ? multiply(Qtotal, blockDiag(Sdiag, N)) : undefined
+
+    return { values: lambdas, C }
+  }
+
+  /**
+   * @param {Matrix} A original matrix
+   * @param {number} N size of A
+   * @param {Matrix} C column transformation matrix that turns A into upper triangular
+   * @param {number[]} values array of eigenvalues of A
+   * @returns {Matrix[]} eigenvalues
+   */
+  function findEigenvectors (A, N, C, values, prec) {
+    const Cinv = inv(C)
+    const U = multiply(Cinv, A, C)
+
+    // turn values into a kind of "multiset"
+    // this way it is easier to find eigenvectors
+    const uniqueValues = []
+    const multiplicities = []
+
+    for (const λ of values) {
+      const i = indexOf(uniqueValues, λ, equal)
+
+      // a dirty trick that helps us find more vectors
+      // TODO with iterative algorithm this can be removed
+      const roundedλ = round(λ, subtract(-1, log10(prec)))
+
+      if (i === -1) {
+        uniqueValues.push(roundedλ)
+        multiplicities.push(1)
+      } else {
+        multiplicities[i] += 1
+      }
+    }
+
+    // find eigenvectors by solving U − λE = 0
+    // TODO replace with an iterative eigenvector algorithm
+    // (this one might fail for imprecise eigenvalues)
+
+    const vectors = []
+    const len = uniqueValues.length
+    const b = Array(N).fill(0)
+    const E = diag(Array(N).fill(1))
+
+    // eigenvalues for which usolve failed (due to numerical error)
+    const failedLambdas = []
+
+    for (let i = 0; i < len; i++) {
+      const λ = uniqueValues[i]
+
+      let solutions = usolveAll(subtract(U, multiply(λ, E)), b)
+      solutions = solutions.map(v => multiply(C, v))
+
+      solutions.shift() // ignore the null vector
+
+      // looks like we missed something
+      if (solutions.length < multiplicities[i]) {
+        failedLambdas.push(λ)
+      }
+
+      vectors.push(...solutions.map(v => flatten(v)))
+    }
+
+    if (failedLambdas.length !== 0) {
+      const err = new Error('Failed to find eigenvectors for the following eigenvalues: ' + failedLambdas.join(', '))
+      err.values = values
+      err.vectors = vectors
+      throw err
+    }
+
+    return vectors
+  }
+
+  /**
+   * Compute the eigenvalues of an 2x2 matrix
+   * @return {[number,number]}
+   */
+  function eigenvalues2x2 (a, b, c, d) {
+    // λ± = ½ trA ± ½ √( tr²A - 4 detA )
+    const trA = addScalar(a, d)
+    const detA = subtract(multiplyScalar(a, d), multiplyScalar(b, c))
+    const x = multiplyScalar(trA, 0.5)
+    const y = multiplyScalar(sqrt(subtract(multiplyScalar(trA, trA), multiplyScalar(4, detA))), 0.5)
+
+    return [addScalar(x, y), subtract(x, y)]
+  }
+
+  /**
+   * For an 2x2 matrix compute the transformation matrix S,
+   * so that SAS⁻¹ is an upper triangular matrix
+   * @return {[[number,number],[number,number]]}
+   * @see https://math.berkeley.edu/~ogus/old/Math_54-05/webfoils/jordan.pdf
+   * @see http://people.math.harvard.edu/~knill/teaching/math21b2004/exhibits/2dmatrices/index.html
+   */
+  function jordanBase2x2 (a, b, c, d, l1, l2, prec, type) {
+    const big = type === 'BigNumber'
+    const cplx = type === 'Complex'
+
+    const zero = big ? bignumber(0) : cplx ? complex(0) : 0
+    const one = big ? bignumber(1) : cplx ? complex(1) : 1
+
+    // matrix is already upper triangular
+    // return an identity matrix
+    if (smaller(abs(c), prec)) {
+      return [[one, zero], [zero, one]]
+    }
+
+    // matrix is diagonalizable
+    // return its eigenvectors as columns
+    if (larger(abs(subtract(l1, l2)), prec)) {
+      return [[subtract(l1, d), subtract(l2, d)], [c, c]]
+    }
+
+    // matrix is not diagonalizable
+    // compute off-diagonal elements of N = A - λI
+    // N₁₂ = 0 ⇒ S = ( N⃗₁, I⃗₁ )
+    // N₁₂ ≠ 0 ⇒ S = ( N⃗₂, I⃗₂ )
+
+    const na = subtract(a, l1)
+    const nb = subtract(b, l1)
+    const nc = subtract(c, l1)
+    const nd = subtract(d, l1)
+
+    if (smaller(abs(nb), prec)) {
+      return [[na, one], [nc, zero]]
+    } else {
+      return [[nb, zero], [nd, one]]
+    }
+  }
+
+  /**
+   * Enlarge the matrix from n×n to N×N, setting the new
+   * elements to 1 on diagonal and 0 elsewhere
+   */
+  function inflateMatrix (arr, N) {
+    // add columns
+    for (let i = 0; i < arr.length; i++) {
+      arr[i].push(...Array(N - arr[i].length).fill(0))
+    }
+
+    // add rows
+    for (let i = arr.length; i < N; i++) {
+      arr.push(Array(N).fill(0))
+      arr[i][i] = 1
+    }
+
+    return arr
+  }
+
+  /**
+   * Create a block-diagonal matrix with the given square matrices on the diagonal
+   * @param {Matrix[] | number[][][]} arr array of matrices to be placed on the diagonal
+   * @param {number} N the size of the resulting matrix
+   */
+  function blockDiag (arr, N) {
+    const M = []
+    for (let i = 0; i < N; i++) {
+      M[i] = Array(N).fill(0)
+    }
+
+    let I = 0
+    for (const sub of arr) {
+      const n = sub.length
+
+      for (let i = 0; i < n; i++) {
+        for (let j = 0; j < n; j++) {
+          M[I + i][I + j] = sub[i][j]
+        }
+      }
+
+      I += n
+    }
+
+    return M
+  }
+
+  /**
+   * Finds the index of an element in an array using a custom equality function
+   * @template T
+   * @param {Array<T>} arr array in which to search
+   * @param {T} el the element to find
+   * @param {function(T, T): boolean} fn the equality function, first argument is an element of `arr`, the second is always `el`
+   * @returns {number} the index of `el`, or -1 when it's not in `arr`
+   */
+  function indexOf (arr, el, fn) {
+    for (let i = 0; i < arr.length; i++) {
+      if (fn(arr[i], el)) {
+        return i
+      }
+    }
+    return -1
+  }
+
+  return main
+}
diff --git a/src/function/matrix/eigs/realSymetric.js b/src/function/matrix/eigs/realSymetric.js
new file mode 100644
index 0000000000..57c215f2c6
--- /dev/null
+++ b/src/function/matrix/eigs/realSymetric.js
@@ -0,0 +1,282 @@
+import { clone } from '../../../utils/object.js'
+
+export function createRealSymmetric ({ config, addScalar, subtract, abs, atan, cos, sin, multiplyScalar, inv, bignumber, multiply, add }) {
+  /**
+   * @param {number[] | BigNumber[]} arr
+   * @param {number} N
+   * @param {number} prec
+   * @param {'number' | 'BigNumber'} type
+   */
+  function main (arr, N, prec = config.epsilon, type) {
+    if (type === 'number') {
+      return diag(arr, prec)
+    }
+
+    if (type === 'BigNumber') {
+      return diagBig(arr, prec)
+    }
+
+    throw TypeError('Unsupported data type: ' + type)
+  }
+
+  // diagonalization implementation for number (efficient)
+  function diag (x, precision) {
+    const N = x.length
+    const e0 = Math.abs(precision / N)
+    let psi
+    let Sij = new Array(N)
+    // Sij is Identity Matrix
+    for (let i = 0; i < N; i++) {
+      Sij[i] = createArray(N, 0)
+      Sij[i][i] = 1.0
+    }
+    // initial error
+    let Vab = getAij(x)
+    while (Math.abs(Vab[1]) >= Math.abs(e0)) {
+      const i = Vab[0][0]
+      const j = Vab[0][1]
+      psi = getTheta(x[i][i], x[j][j], x[i][j])
+      x = x1(x, psi, i, j)
+      Sij = Sij1(Sij, psi, i, j)
+      Vab = getAij(x)
+    }
+    const Ei = createArray(N, 0) // eigenvalues
+    for (let i = 0; i < N; i++) {
+      Ei[i] = x[i][i]
+    }
+    return sorting(clone(Ei), clone(Sij))
+  }
+
+  // diagonalization implementation for bigNumber
+  function diagBig (x, precision) {
+    const N = x.length
+    const e0 = abs(precision / N)
+    let psi
+    let Sij = new Array(N)
+    // Sij is Identity Matrix
+    for (let i = 0; i < N; i++) {
+      Sij[i] = createArray(N, 0)
+      Sij[i][i] = 1.0
+    }
+    // initial error
+    let Vab = getAijBig(x)
+    while (abs(Vab[1]) >= abs(e0)) {
+      const i = Vab[0][0]
+      const j = Vab[0][1]
+      psi = getThetaBig(x[i][i], x[j][j], x[i][j])
+      x = x1Big(x, psi, i, j)
+      Sij = Sij1Big(Sij, psi, i, j)
+      Vab = getAijBig(x)
+    }
+    const Ei = createArray(N, 0) // eigenvalues
+    for (let i = 0; i < N; i++) {
+      Ei[i] = x[i][i]
+    }
+    // return [clone(Ei), clone(Sij)]
+    return sorting(clone(Ei), clone(Sij))
+  }
+
+  // get angle
+  function getTheta (aii, ajj, aij) {
+    const denom = (ajj - aii)
+    if (Math.abs(denom) <= config.epsilon) {
+      return Math.PI / 4.0
+    } else {
+      return 0.5 * Math.atan(2.0 * aij / (ajj - aii))
+    }
+  }
+
+  // get angle
+  function getThetaBig (aii, ajj, aij) {
+    const denom = subtract(ajj, aii)
+    if (abs(denom) <= config.epsilon) {
+      return bignumber(-1).acos().div(4)
+    } else {
+      return multiplyScalar(0.5, atan(multiply(2.0, aij, inv(denom))))
+    }
+  }
+
+  // update eigvec
+  function Sij1 (Sij, theta, i, j) {
+    const N = Sij.length
+    const c = Math.cos(theta)
+    const s = Math.sin(theta)
+    const Ski = createArray(N, 0)
+    const Skj = createArray(N, 0)
+    for (let k = 0; k < N; k++) {
+      Ski[k] = c * Sij[k][i] - s * Sij[k][j]
+      Skj[k] = s * Sij[k][i] + c * Sij[k][j]
+    }
+    for (let k = 0; k < N; k++) {
+      Sij[k][i] = Ski[k]
+      Sij[k][j] = Skj[k]
+    }
+    return Sij
+  }
+  // update eigvec for overlap
+  function Sij1Big (Sij, theta, i, j) {
+    const N = Sij.length
+    const c = cos(theta)
+    const s = sin(theta)
+    const Ski = createArray(N, bignumber(0))
+    const Skj = createArray(N, bignumber(0))
+    for (let k = 0; k < N; k++) {
+      Ski[k] = subtract(multiplyScalar(c, Sij[k][i]), multiplyScalar(s, Sij[k][j]))
+      Skj[k] = addScalar(multiplyScalar(s, Sij[k][i]), multiplyScalar(c, Sij[k][j]))
+    }
+    for (let k = 0; k < N; k++) {
+      Sij[k][i] = Ski[k]
+      Sij[k][j] = Skj[k]
+    }
+    return Sij
+  }
+
+  // update matrix
+  function x1Big (Hij, theta, i, j) {
+    const N = Hij.length
+    const c = bignumber(cos(theta))
+    const s = bignumber(sin(theta))
+    const c2 = multiplyScalar(c, c)
+    const s2 = multiplyScalar(s, s)
+    const Aki = createArray(N, bignumber(0))
+    const Akj = createArray(N, bignumber(0))
+    // 2cs Hij
+    const csHij = multiply(bignumber(2), c, s, Hij[i][j])
+    //  Aii
+    const Aii = addScalar(subtract(multiplyScalar(c2, Hij[i][i]), csHij), multiplyScalar(s2, Hij[j][j]))
+    const Ajj = add(multiplyScalar(s2, Hij[i][i]), csHij, multiplyScalar(c2, Hij[j][j]))
+    // 0  to i
+    for (let k = 0; k < N; k++) {
+      Aki[k] = subtract(multiplyScalar(c, Hij[i][k]), multiplyScalar(s, Hij[j][k]))
+      Akj[k] = addScalar(multiplyScalar(s, Hij[i][k]), multiplyScalar(c, Hij[j][k]))
+    }
+    // Modify Hij
+    Hij[i][i] = Aii
+    Hij[j][j] = Ajj
+    Hij[i][j] = bignumber(0)
+    Hij[j][i] = bignumber(0)
+    // 0  to i
+    for (let k = 0; k < N; k++) {
+      if (k !== i && k !== j) {
+        Hij[i][k] = Aki[k]
+        Hij[k][i] = Aki[k]
+        Hij[j][k] = Akj[k]
+        Hij[k][j] = Akj[k]
+      }
+    }
+    return Hij
+  }
+
+  // update matrix
+  function x1 (Hij, theta, i, j) {
+    const N = Hij.length
+    const c = Math.cos(theta)
+    const s = Math.sin(theta)
+    const c2 = c * c
+    const s2 = s * s
+    const Aki = createArray(N, 0)
+    const Akj = createArray(N, 0)
+    //  Aii
+    const Aii = c2 * Hij[i][i] - 2 * c * s * Hij[i][j] + s2 * Hij[j][j]
+    const Ajj = s2 * Hij[i][i] + 2 * c * s * Hij[i][j] + c2 * Hij[j][j]
+    // 0  to i
+    for (let k = 0; k < N; k++) {
+      Aki[k] = c * Hij[i][k] - s * Hij[j][k]
+      Akj[k] = s * Hij[i][k] + c * Hij[j][k]
+    }
+    // Modify Hij
+    Hij[i][i] = Aii
+    Hij[j][j] = Ajj
+    Hij[i][j] = 0
+    Hij[j][i] = 0
+    // 0  to i
+    for (let k = 0; k < N; k++) {
+      if (k !== i && k !== j) {
+        Hij[i][k] = Aki[k]
+        Hij[k][i] = Aki[k]
+        Hij[j][k] = Akj[k]
+        Hij[k][j] = Akj[k]
+      }
+    }
+    return Hij
+  }
+
+  // get max off-diagonal value from Upper Diagonal
+  function getAij (Mij) {
+    const N = Mij.length
+    let maxMij = 0
+    let maxIJ = [0, 1]
+    for (let i = 0; i < N; i++) {
+      for (let j = i + 1; j < N; j++) {
+        if (Math.abs(maxMij) < Math.abs(Mij[i][j])) {
+          maxMij = Math.abs(Mij[i][j])
+          maxIJ = [i, j]
+        }
+      }
+    }
+    return [maxIJ, maxMij]
+  }
+
+  // get max off-diagonal value from Upper Diagonal
+  function getAijBig (Mij) {
+    const N = Mij.length
+    let maxMij = 0
+    let maxIJ = [0, 1]
+    for (let i = 0; i < N; i++) {
+      for (let j = i + 1; j < N; j++) {
+        if (abs(maxMij) < abs(Mij[i][j])) {
+          maxMij = abs(Mij[i][j])
+          maxIJ = [i, j]
+        }
+      }
+    }
+    return [maxIJ, maxMij]
+  }
+
+  // sort results
+  function sorting (E, S) {
+    const N = E.length
+    const values = Array(N)
+    const vectors = Array(N)
+
+    for (let k = 0; k < N; k++) {
+      vectors[k] = Array(N)
+    }
+    for (let i = 0; i < N; i++) {
+      let minID = 0
+      let minE = E[0]
+      for (let j = 0; j < E.length; j++) {
+        if (abs(E[j]) < abs(minE)) {
+          minID = j
+          minE = E[minID]
+        }
+      }
+      values[i] = E.splice(minID, 1)[0]
+      for (let k = 0; k < N; k++) {
+        vectors[k][i] = S[k][minID]
+        S[k].splice(minID, 1)
+      }
+    }
+
+    return { values, vectors }
+  }
+
+  /**
+   * Create an array of a certain size and fill all items with an initial value
+   * @param {number} size
+   * @param {number} value
+   * @return {number[]}
+   */
+  function createArray (size, value) {
+    // TODO: as soon as all browsers support Array.fill, use that instead (IE doesn't support it)
+    const array = new Array(size)
+
+    for (let i = 0; i < size; i++) {
+      array[i] = value
+    }
+
+    return array
+  }
+
+  return main
+}
diff --git a/src/utils/array.js b/src/utils/array.js
index 0a275b4955..cd434ab63b 100644
--- a/src/utils/array.js
+++ b/src/utils/array.js
@@ -551,7 +551,7 @@ export function generalize (a) {
  * This method does not validate Array Matrix shape
  * @param {Array} array
  * @param {function} typeOf   Callback function to use to determine the type of a value
- * @return string
+ * @return {string}
  */
 export function getArrayDataType (array, typeOf) {
   let type // to hold type info
diff --git a/test/unit-tests/function/matrix/eigs.test.js b/test/unit-tests/function/matrix/eigs.test.js
index e100765ba8..84846100e6 100644
--- a/test/unit-tests/function/matrix/eigs.test.js
+++ b/test/unit-tests/function/matrix/eigs.test.js
@@ -2,22 +2,20 @@ import assert from 'assert'
 import math from '../../../../src/defaultInstance.js'
 import approx from '../../../../tools/approx.js'
 const eigs = math.eigs
+const complex = math.complex
 
 describe('eigs', function () {
-  it('should only accept a square matrix', function () {
+  it('only accepts a square matrix', function () {
     assert.throws(function () { eigs(math.matrix([[1, 2, 3], [4, 5, 6]])) }, /Matrix must be square/)
     assert.throws(function () { eigs([[1, 2, 3], [4, 5, 6]]) }, /Matrix must be square/)
     assert.throws(function () { eigs([[1, 2], [4, 5, 6]]) }, /DimensionError: Dimension mismatch/)
     assert.throws(function () { eigs([4, 5, 6]) }, /Matrix must be square/)
     assert.throws(function () { eigs(1.0) }, /TypeError: Unexpected type of argument/)
     assert.throws(function () { eigs('random') }, /TypeError: Unexpected type of argument/)
-    assert.throws(function () { eigs(math.matrix([[1, 2], [2.1, 3]])) }, /Input matrix is not symmetric/)
   })
 
-  it('should only accept a matrix with valid element type', function () {
-    assert.throws(function () { eigs([['x', 2], [4, 5]]) }, /Mixed matrix element type is not supported/)
-    assert.throws(function () { eigs([[1, 2], [2, '5']]) }, /Mixed matrix element type is not supported/)
-    assert.throws(function () { eigs([['1', '2'], ['2', '5']]) }, /Matrix element type not supported/)
+  it('only accepts a matrix with valid element type', function () {
+    assert.throws(function () { eigs([['x', 2], [4, 5]]) }, /Cannot convert "x" to a number/)
   })
 
   it('eigenvalue check for diagonal matrix', function () {
@@ -28,22 +26,25 @@ describe('eigs', function () {
     approx.deepEqual(eigs(
       [[2, 0, 0], [0, 1, 0], [0, 0, 5]]).values, [1, 2, 5]
     )
+    approx.deepEqual(eigs(
+      [[complex(2, 1), 0, 0], [0, 1, 0], [0, 0, complex(0, 5)]]).values, [complex(1, 0), complex(2, 1), complex(0, 5)]
+    )
   })
 
-  it('eigenvalue check for 2x2 simple matrix', function () {
+  it('calculates eigenvalues for 2x2 simple matrix', function () {
     // 2x2 test
     approx.deepEqual(eigs(
       [[1, 0.1], [0.1, 1]]).values, [0.9, 1.1]
     )
     approx.deepEqual(eigs(
-      math.matrix([[1, 0.1], [0.1, 1]])).values, math.matrix([0.9, 1.1])
+      math.matrix([[1, 0.1], [0.1, 1]])).values, [0.9, 1.1]
     )
     approx.deepEqual(eigs(
       [[5, 2.3], [2.3, 1]]).values, [-0.04795013082563382, 6.047950130825635]
     )
   })
 
-  it('eigenvalue check for 3x3 and 4x4 matrix', function () {
+  it('calculates eigenvalues for 3x3 and 4x4 matrix', function () {
     // 3x3 test and 4x4
     approx.deepEqual(eigs(
       [[1.0, 1.0, 1.0],
@@ -56,7 +57,7 @@ describe('eigs', function () {
         [-3.8571699139231796, 0.7047577966772156, 0.9122549659760404, 0.9232933211541949],
         [2.852995822026198, 0.9122549659760404, 1.6598316026960402, -1.2931270747054358],
         [4.1957619745869845, 0.9232933211541949, -1.2931270747054358, -4.665994662426116]]).values,
-    [-8.687249803623432, -0.9135495807127523, 2.26552473288741, 5.6502090685149735]
+    [-0.9135495807127523, 2.26552473288741, 5.6502090685149735, -8.687249803623432]
     )
   })
 
@@ -78,7 +79,7 @@ describe('eigs', function () {
     approx.deepEqual(Ei, E)
   })
 
-  it('fractions are supported', function () {
+  it('supports fractions', function () {
     const aij = math.fraction('1/2')
     approx.deepEqual(eigs(
       [[aij, aij, aij],
@@ -88,7 +89,7 @@ describe('eigs', function () {
     )
   })
 
-  it('bigNumber diagonalization is supported', function () {
+  it('diagonalizes matrix with bigNumber', function () {
     const x = [[math.bignumber(1), math.bignumber(0)], [math.bignumber(0), math.bignumber(1)]]
     approx.deepEqual(eigs(x).values, [math.bignumber(1), math.bignumber(1)])
     const y = [[math.bignumber(1), math.bignumber(1.0)], [math.bignumber(1.0), math.bignumber(1)]]
@@ -112,7 +113,7 @@ describe('eigs', function () {
     approx.deepEqual(Ei, E)
   })
 
-  it('make sure BigNumbers input is actually calculated with BigNumber precision', function () {
+  it('actually calculates BigNumbers input with BigNumber precision', function () {
     const B = math.bignumber([
       [0, 1],
       [1, 0]