diff --git a/NEWS.md b/NEWS.md
index b261a65620b2d..cdf940755907f 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -381,6 +381,10 @@ Deprecated or removed
   * The `cholfact`/`cholfact!` methods that accepted an `uplo` symbol have been deprecated
     in favor of using `Hermitian` (or `Symmetric`) views ([#22187], [#22188]).
 
+  * The `thin` keyword argument for orthogonal decomposition methods has
+    been deprecated in favor of `full`, which has the opposite meaning:
+    `thin == true` if and only if `full == false` ([#24279]).
+
   * `isposdef(A::AbstractMatrix, UL::Symbol)` and `isposdef!(A::AbstractMatrix, UL::Symbol)`
     have been deprecated in favor of `isposdef(Hermitian(A, UL))` and `isposdef!(Hermitian(A, UL))`
     respectively ([#22245]).
diff --git a/base/deprecated.jl b/base/deprecated.jl
index 2236f3c8081d7..6ba9a4106530f 100644
--- a/base/deprecated.jl
+++ b/base/deprecated.jl
@@ -2031,6 +2031,11 @@ end
 @deprecate strwidth textwidth
 @deprecate charwidth textwidth
 
+# TODO: after 0.7, remove thin keyword argument and associated logic from...
+# (1) base/linalg/svd.jl
+# (2) base/linalg/qr.jl
+# (3) base/linalg/lq.jl
+
 @deprecate find(x::Number)            find(!iszero, x)
 @deprecate findnext(A, v, i::Integer) findnext(equalto(v), A, i)
 @deprecate findfirst(A, v)            findfirst(equalto(v), A)
diff --git a/base/linalg/bidiag.jl b/base/linalg/bidiag.jl
index e9abd67a17dfd..4a1f05ab222ef 100644
--- a/base/linalg/bidiag.jl
+++ b/base/linalg/bidiag.jl
@@ -182,11 +182,27 @@ similar(B::Bidiagonal, ::Type{T}, dims::Union{Dims{1},Dims{2}}) where {T} = spze
 
 #Singular values
 svdvals!(M::Bidiagonal{<:BlasReal}) = LAPACK.bdsdc!(M.uplo, 'N', M.dv, M.ev)[1]
-function svdfact!(M::Bidiagonal{<:BlasReal}; thin::Bool=true)
+function svdfact!(M::Bidiagonal{<:BlasReal}; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact!(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact!(A; full = $(!thin))`."), :svdfact!)
+        full::Bool = !thin
+    end
     d, e, U, Vt, Q, iQ = LAPACK.bdsdc!(M.uplo, 'I', M.dv, M.ev)
     SVD(U, d, Vt)
 end
-svdfact(M::Bidiagonal; thin::Bool=true) = svdfact!(copy(M),thin=thin)
+function svdfact(M::Bidiagonal; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+        full::Bool = !thin
+    end
+    return svdfact!(copy(M), full = full)
+end
 
 ####################
 # Generic routines #
diff --git a/base/linalg/dense.jl b/base/linalg/dense.jl
index 95b9983635149..7545cff6a7275 100644
--- a/base/linalg/dense.jl
+++ b/base/linalg/dense.jl
@@ -1263,7 +1263,7 @@ function pinv(A::StridedMatrix{T}, tol::Real) where T
             return B
         end
     end
-    SVD         = svdfact(A, thin=true)
+    SVD         = svdfact(A, full = false)
     Stype       = eltype(SVD.S)
     Sinv        = zeros(Stype, length(SVD.S))
     index       = SVD.S .> tol*maximum(SVD.S)
@@ -1305,7 +1305,7 @@ julia> nullspace(M)
 function nullspace(A::StridedMatrix{T}) where T
     m, n = size(A)
     (m == 0 || n == 0) && return eye(T, n)
-    SVD = svdfact(A, thin = false)
+    SVD = svdfact(A, full = true)
     indstart = sum(SVD.S .> max(m,n)*maximum(SVD.S)*eps(eltype(SVD.S))) + 1
     return SVD.Vt[indstart:end,:]'
 end
diff --git a/base/linalg/lq.jl b/base/linalg/lq.jl
index 66dcff8ebf770..76b526c3769af 100644
--- a/base/linalg/lq.jl
+++ b/base/linalg/lq.jl
@@ -33,24 +33,31 @@ lqfact(A::StridedMatrix{<:BlasFloat})  = lqfact!(copy(A))
 lqfact(x::Number) = lqfact(fill(x,1,1))
 
 """
-    lq(A; [thin=true]) -> L, Q
+    lq(A; full = false) -> L, Q
 
-Perform an LQ factorization of `A` such that `A = L*Q`. The default is to compute
-a "thin" factorization. The LQ factorization is the QR factorization of `A.'`.
-`L` is not extendedwith zeros if the explicit, square form of `Q`
-is requested via `thin = false`.
+Perform an LQ factorization of `A` such that `A = L*Q`. The default (`full = false`)
+computes a factorization with possibly-rectangular `L` and `Q`, commonly the "thin"
+factorization. The LQ factorization is the QR factorization of `A.'`. If the explicit,
+full/square form of `Q` is requested via `full = true`, `L` is not extended with zeros.
 
 !!! note
     While in QR factorization the "thin" factorization is so named due to yielding
-    either a square or "tall"/"thin" factor `Q`, in LQ factorization the "thin"
-    factorization somewhat confusingly produces either a square or "short"/"wide"
-    factor `Q`. "Thin" factorizations more broadly are also (more descriptively)
-    referred to as "truncated" or "reduced" factorizatons.
+    either a square or "tall"/"thin" rectangular factor `Q`, in LQ factorization the
+    "thin" factorization somewhat confusingly produces either a square or "short"/"wide"
+    rectangular factor `Q`. "Thin" factorizations more broadly are also
+    referred to as "reduced" factorizatons.
 """
-function lq(A::Union{Number,AbstractMatrix}; thin::Bool = true)
+function lq(A::Union{Number,AbstractMatrix}; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `lq(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `lq(A; full = $(!thin))`."), :lq)
+        full::Bool = !thin
+    end
     F = lqfact(A)
     L, Q = F[:L], F[:Q]
-    return L, thin ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 2)))
+    return L, !full ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 2)))
 end
 
 copy(A::LQ) = LQ(copy(A.factors), copy(A.τ))
diff --git a/base/linalg/qr.jl b/base/linalg/qr.jl
index b83cb0351261a..fbe1cc8876329 100644
--- a/base/linalg/qr.jl
+++ b/base/linalg/qr.jl
@@ -265,7 +265,7 @@ The following functions are available for the `QR` objects: [`inv`](@ref), [`siz
 and [`\\`](@ref). When `A` is rectangular, `\\` will return a least squares
 solution and if the solution is not unique, the one with smallest norm is returned.
 
-Multiplication with respect to either thin or full `Q` is allowed, i.e. both `F[:Q]*F[:R]`
+Multiplication with respect to either full/square or non-full/square `Q` is allowed, i.e. both `F[:Q]*F[:R]`
 and `F[:Q]*A` are supported. A `Q` matrix can be converted into a regular matrix with
 [`Matrix`](@ref).
 
@@ -305,24 +305,33 @@ end
 qrfact(x::Number) = qrfact(fill(x,1,1))
 
 """
-    qr(A, pivot=Val(false); thin::Bool=true) -> Q, R, [p]
+    qr(A, pivot=Val(false); full::Bool = false) -> Q, R, [p]
 
 Compute the (pivoted) QR factorization of `A` such that either `A = Q*R` or `A[:,p] = Q*R`.
 Also see [`qrfact`](@ref).
-The default is to compute a thin factorization. Note that `R` is not
-extended with zeros when the full `Q` is requested.
+The default is to compute a "thin" factorization. Note that `R` is not
+extended with zeros when a full/square orthogonal factor `Q` is requested (via `full = true`).
 """
-qr(A::Union{Number, AbstractMatrix}, pivot::Union{Val{false}, Val{true}}=Val(false); thin::Bool=true) =
-    _qr(A, pivot, thin=thin)
-function _qr(A::Union{Number, AbstractMatrix}, ::Val{false}; thin::Bool=true)
+function qr(A::Union{Number,AbstractMatrix}, pivot::Union{Val{false},Val{true}} = Val(false);
+            full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `qr(A, pivot; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `qr(A, pivot; full = $(!thin))`."), :qr)
+        full::Bool = !thin
+    end
+    return _qr(A, pivot, full = full)
+end
+function _qr(A::Union{Number,AbstractMatrix}, ::Val{false}; full::Bool = false)
     F = qrfact(A, Val(false))
     Q, R = getq(F), F[:R]::Matrix{eltype(F)}
-    return (thin ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))), R
+    return (!full ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))), R
 end
-function _qr(A::Union{Number, AbstractMatrix}, ::Val{true}; thin::Bool=true)
+function _qr(A::Union{Number, AbstractMatrix}, ::Val{true}; full::Bool = false)
     F = qrfact(A, Val(true))
     Q, R, p = getq(F), F[:R]::Matrix{eltype(F)}, F[:p]::Vector{BlasInt}
-    return (thin ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))), R, p
+    return (!full ? Array(Q) : A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))), R, p
 end
 
 """
diff --git a/base/linalg/svd.jl b/base/linalg/svd.jl
index 6b4ace6cce2d3..c1dcdac06757d 100644
--- a/base/linalg/svd.jl
+++ b/base/linalg/svd.jl
@@ -11,23 +11,30 @@ end
 SVD(U::AbstractArray{T}, S::Vector{Tr}, Vt::AbstractArray{T}) where {T,Tr} = SVD{T,Tr,typeof(U)}(U, S, Vt)
 
 """
-    svdfact!(A, thin::Bool=true) -> SVD
+    svdfact!(A; full::Bool = false) -> SVD
 
 `svdfact!` is the same as [`svdfact`](@ref), but saves space by
 overwriting the input `A`, instead of creating a copy.
 """
-function svdfact!(A::StridedMatrix{T}; thin::Bool=true) where T<:BlasFloat
+function svdfact!(A::StridedMatrix{T}; full::Bool = false, thin::Union{Bool,Void} = nothing) where T<:BlasFloat
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact!(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact!(A; full = $(!thin))`."), :svdfact!)
+        full::Bool = !thin
+    end
     m,n = size(A)
     if m == 0 || n == 0
-        u,s,vt = (eye(T, m, thin ? n : m), real(zeros(T,0)), eye(T,n,n))
+        u,s,vt = (eye(T, m, full ? m : n), real(zeros(T,0)), eye(T,n,n))
     else
-        u,s,vt = LAPACK.gesdd!(thin ? 'S' : 'A', A)
+        u,s,vt = LAPACK.gesdd!(full ? 'A' : 'S', A)
     end
     SVD(u,s,vt)
 end
 
 """
-    svdfact(A; thin::Bool=true) -> SVD
+    svdfact(A; full::Bool = false) -> SVD
 
 Compute the singular value decomposition (SVD) of `A` and return an `SVD` object.
 
@@ -36,9 +43,9 @@ Compute the singular value decomposition (SVD) of `A` and return an `SVD` object
 The algorithm produces `Vt` and hence `Vt` is more efficient to extract than `V`.
 The singular values in `S` are sorted in descending order.
 
-If `thin=true` (default), a thin SVD is returned. For a ``M \\times N`` matrix
-`A`, `U` is ``M \\times M`` for a full SVD (`thin=false`) and
-``M \\times \\min(M, N)`` for a thin SVD.
+If `full = false` (default), a "thin" SVD is returned. For a
+``M \\times N`` matrix `A`, `U` is ``M \\times M`` for a "full" SVD (`full = true`) and
+``M \\times \\min(M, N)`` for a "thin" SVD.
 
 # Examples
 ```jldoctest
@@ -59,22 +66,47 @@ julia> F[:U] * Diagonal(F[:S]) * F[:Vt]
  0.0  2.0  0.0  0.0  0.0
 ```
 """
-function svdfact(A::StridedVecOrMat{T}; thin::Bool = true) where T
+function svdfact(A::StridedVecOrMat{T}; full::Bool = false, thin::Union{Bool,Void} = nothing) where T
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+        full::Bool = !thin
+    end
     S = promote_type(Float32, typeof(one(T)/norm(one(T))))
-    svdfact!(copy_oftype(A, S), thin = thin)
+    svdfact!(copy_oftype(A, S), full = full)
+end
+function svdfact(x::Number; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+        full::Bool = !thin
+    end
+    return SVD(x == 0 ? fill(one(x), 1, 1) : fill(x/abs(x), 1, 1), [abs(x)], fill(one(x), 1, 1))
+end
+function svdfact(x::Integer; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+        full::Bool = !thin
+    end
+    return svdfact(float(x), full = full)
 end
-svdfact(x::Number; thin::Bool=true) = SVD(x == 0 ? fill(one(x), 1, 1) : fill(x/abs(x), 1, 1), [abs(x)], fill(one(x), 1, 1))
-svdfact(x::Integer; thin::Bool=true) = svdfact(float(x), thin=thin)
 
 """
-    svd(A; thin::Bool=true) -> U, S, V
+    svd(A; full::Bool = false) -> U, S, V
 
 Computes the SVD of `A`, returning `U`, vector `S`, and `V` such that
 `A == U * Diagonal(S) * V'`. The singular values in `S` are sorted in descending order.
 
-If `thin = true` (default), a thin SVD is returned. For a ``M \\times N`` matrix
-`A`, `U` is ``M \\times M`` for a full SVD (`thin=false`) and
-``M \\times \\min(M, N)`` for a thin SVD.
+If `full = false` (default), a "thin" SVD is returned. For a ``M \\times N`` matrix
+`A`, `U` is ``M \\times M`` for a "full" SVD (`full = true`) and
+``M \\times \\min(M, N)`` for a "thin" SVD.
 
 `svd` is a wrapper around [`svdfact`](@ref), extracting all parts
 of the `SVD` factorization to a tuple. Direct use of `svdfact` is therefore more
@@ -99,11 +131,27 @@ julia> U * Diagonal(S) * V'
  0.0  2.0  0.0  0.0  0.0
 ```
 """
-function svd(A::AbstractArray; thin::Bool=true)
-    F = svdfact(A, thin=thin)
+function svd(A::AbstractArray; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svd(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g `svd(A; full = $(!thin))`."), :svd)
+        full::Bool = !thin
+    end
+    F = svdfact(A, full = full)
     F.U, F.S, F.Vt'
 end
-svd(x::Number; thin::Bool=true) = first.(svd(fill(x, 1, 1)))
+function svd(x::Number; full::Bool = false, thin::Union{Bool,Void} = nothing)
+    # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
+    if thin != nothing
+        Base.depwarn(string("the `thin` keyword argument in `svd(A; thin = $(thin))` has ",
+            "been deprecated in favor of `full`, which has the opposite meaning, ",
+            "e.g. `svd(A; full = $(!thin))`."), :svd)
+        full::Bool = !thin
+    end
+    return first.(svd(fill(x, 1, 1)))
+end
 
 function getindex(F::SVD, d::Symbol)
     if d == :U
diff --git a/test/linalg/lq.jl b/test/linalg/lq.jl
index 7f487e977fc12..b7c2b2708ecc1 100644
--- a/test/linalg/lq.jl
+++ b/test/linalg/lq.jl
@@ -22,7 +22,7 @@ bimg  = randn(n,2)/2
 
 # helper functions to unambiguously recover explicit forms of an LQPackedQ
 squareQ(Q::LinAlg.LQPackedQ) = A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 2)))
-truncatedQ(Q::LinAlg.LQPackedQ) = convert(Array, Q)
+rectangularQ(Q::LinAlg.LQPackedQ) = convert(Array, Q)
 
 @testset for eltya in (Float32, Float64, Complex64, Complex128)
     a = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(areal, aimg) : areal)
@@ -98,10 +98,10 @@ truncatedQ(Q::LinAlg.LQPackedQ) = convert(Array, Q)
         @testset "Matmul with LQ factorizations" begin
             lqa = lqfact(a[:,1:n1])
             l,q = lqa[:L], lqa[:Q]
-            @test truncatedQ(q)*truncatedQ(q)' ≈ eye(eltya,n1)
+            @test rectangularQ(q)*rectangularQ(q)' ≈ eye(eltya,n1)
             @test squareQ(q)'*squareQ(q) ≈ eye(eltya, n1)
             @test_throws DimensionMismatch A_mul_B!(eye(eltya,n+1),q)
-            @test Ac_mul_B!(q, truncatedQ(q)) ≈ eye(eltya,n1)
+            @test Ac_mul_B!(q, rectangularQ(q)) ≈ eye(eltya,n1)
             @test_throws DimensionMismatch A_mul_Bc!(eye(eltya,n+1),q)
             @test_throws BoundsError size(q,-1)
         end
@@ -111,14 +111,14 @@ end
 @testset "correct form of Q from lq(...) (#23729)" begin
     # where the original matrix (say A) is square or has more rows than columns,
     # then A's factorization's triangular factor (say L) should have the same shape
-    # as A independent of factorization form (truncated, square), and A's factorization's
+    # as A independent of factorization form ("full", "reduced"/"thin"), and A's factorization's
     # orthogonal factor (say Q) should be a square matrix of order of A's number of
-    # columns independent of factorization form (truncated, square), and L and Q
+    # columns independent of factorization form ("full", "reduced"/"thin"), and L and Q
     # should have multiplication-compatible shapes.
     local m, n = 4, 2
     A = randn(m, n)
-    for thin in (true, false)
-        L, Q = lq(A, thin = thin)
+    for full in (false, true)
+        L, Q = lq(A, full = full)
         @test size(L) == (m, n)
         @test size(Q) == (n, n)
         @test isapprox(A, L*Q)
@@ -126,23 +126,23 @@ end
     # where the original matrix has strictly fewer rows than columns ...
     m, n = 2, 4
     A = randn(m, n)
-    # ... then, for a truncated factorization of A, L should be a square matrix
+    # ... then, for a rectangular/"thin" factorization of A, L should be a square matrix
     # of order of A's number of rows, Q should have the same shape as A,
     # and L and Q should have multiplication-compatible shapes
-    Lthin, Qthin = lq(A, thin = true)
-    @test size(Lthin) == (m, m)
-    @test size(Qthin) == (m, n)
-    @test isapprox(A, Lthin * Qthin)
-    # ... and, for a square/non-truncated factorization of A, L should have the
+    Lrect, Qrect = lq(A, full = false)
+    @test size(Lrect) == (m, m)
+    @test size(Qrect) == (m, n)
+    @test isapprox(A, Lrect * Qrect)
+    # ... and, for a full factorization of A, L should have the
     # same shape as A, Q should be a square matrix of order of A's number of columns,
     # and L and Q should have multiplication-compatible shape. but instead the L returned
-    # has no zero-padding on the right / is L for the truncated factorization,
+    # has no zero-padding on the right / is L for the rectangular/"thin" factorization,
     # so for L and Q to have multiplication-compatible shapes, L must be zero-padded
     # to have the shape of A.
-    Lsquare, Qsquare = lq(A, thin = false)
-    @test size(Lsquare) == (m, m)
-    @test size(Qsquare) == (n, n)
-    @test isapprox(A, [Lsquare zeros(m, n - m)] * Qsquare)
+    Lfull, Qfull = lq(A, full = true)
+    @test size(Lfull) == (m, m)
+    @test size(Qfull) == (n, n)
+    @test isapprox(A, [Lfull zeros(m, n - m)] * Qfull)
 end
 
 @testset "getindex on LQPackedQ (#23733)" begin
@@ -153,14 +153,14 @@ end
         return implicitQ, explicitQ
     end
 
-    m, n = 3, 3 # truncated Q 3-by-3, square Q 3-by-3
+    m, n = 3, 3 # reduced Q 3-by-3, full Q 3-by-3
     implicitQ, explicitQ = getqs(lqfact(randn(m, n)))
     @test implicitQ[1, 1] == explicitQ[1, 1]
     @test implicitQ[m, 1] == explicitQ[m, 1]
     @test implicitQ[1, n] == explicitQ[1, n]
     @test implicitQ[m, n] == explicitQ[m, n]
 
-    m, n = 3, 4 # truncated Q 3-by-4, square Q 4-by-4
+    m, n = 3, 4 # reduced Q 3-by-4, full Q 4-by-4
     implicitQ, explicitQ = getqs(lqfact(randn(m, n)))
     @test implicitQ[1, 1] == explicitQ[1, 1]
     @test implicitQ[m, 1] == explicitQ[m, 1]
@@ -169,7 +169,7 @@ end
     @test implicitQ[m+1, 1] == explicitQ[m+1, 1]
     @test implicitQ[m+1, n] == explicitQ[m+1, n]
 
-    m, n = 4, 3 # truncated Q 3-by-3, square Q 3-by-3
+    m, n = 4, 3 # reduced Q 3-by-3, full Q 3-by-3
     implicitQ, explicitQ = getqs(lqfact(randn(m, n)))
     @test implicitQ[1, 1] == explicitQ[1, 1]
     @test implicitQ[n, 1] == explicitQ[n, 1]
@@ -178,11 +178,11 @@ end
 end
 
 @testset "size on LQPackedQ (#23780)" begin
-    # size(Q::LQPackedQ) yields the shape of Q's square form
+    # size(Q::LQPackedQ) yields the shape of Q's full/square form
     for ((mA, nA), nQ) in (
-        ((3, 3), 3), # A 3-by-3 => square Q 3-by-3
-        ((3, 4), 4), # A 3-by-4 => square Q 4-by-4
-        ((4, 3), 3) )# A 4-by-3 => square Q 3-by-3
+        ((3, 3), 3), # A 3-by-3 => full/square Q 3-by-3
+        ((3, 4), 4), # A 3-by-4 => full/square Q 4-by-4
+        ((4, 3), 3) )# A 4-by-3 => full/square Q 3-by-3
         @test size(lqfact(randn(mA, nA))[:Q]) == (nQ, nQ)
     end
 end
@@ -205,12 +205,12 @@ end
         @test Ac_mul_Bc(C, implicitQ) ≈ Ac_mul_Bc(C, explicitQ)
     end
     # where the LQ-factored matrix has at least as many rows m as columns n,
-    # Q's square and truncated forms have the same shape (n-by-n). hence we expect
+    # Q's full/square and reduced/rectangular forms have the same shape (n-by-n). hence we expect
     # _only_ *-by-n (n-by-*) C to work in A_mul_B*(C, Q) (Ac_mul_B*(C, Q)) ops.
     # and hence the n-by-n C tests above suffice.
     #
     # where the LQ-factored matrix has more columns n than rows m,
-    # Q's square form is n-by-n whereas its truncated form is m-by-n.
+    # Q's full/square form is n-by-n whereas its reduced/rectangular form is m-by-n.
     # hence we need also test *-by-m C with
     # A*_mul_B(C, Q) ops, as below via m-by-m C.
     mA, nA = 3, 4
diff --git a/test/linalg/qr.jl b/test/linalg/qr.jl
index 94f0e95d06742..2bf60515051e0 100644
--- a/test/linalg/qr.jl
+++ b/test/linalg/qr.jl
@@ -21,7 +21,7 @@ bimg  = randn(n,2)/2
 
 # helper functions to unambiguously recover explicit forms of an implicit QR Q
 squareQ(Q::LinAlg.AbstractQ) = A_mul_B!(Q, eye(eltype(Q), size(Q.factors, 1)))
-truncatedQ(Q::LinAlg.AbstractQ) = convert(Array, Q)
+rectangularQ(Q::LinAlg.AbstractQ) = convert(Array, Q)
 
 @testset for eltya in (Float32, Float64, Complex64, Complex128, BigFloat, Int)
     raw_a = eltya == Int ? rand(1:7, n, n) : convert(Matrix{eltya}, eltya <: Complex ? complex.(areal, aimg) : areal)
@@ -75,9 +75,9 @@ truncatedQ(Q::LinAlg.AbstractQ) = convert(Array, Q)
                 q,r   = qra[:Q], qra[:R]
                 @test_throws KeyError qra[:Z]
                 @test q'*squareQ(q) ≈ eye(a_1)
-                @test q'*truncatedQ(q) ≈ eye(a_1, n1)
+                @test q'*rectangularQ(q) ≈ eye(a_1, n1)
                 @test q*r ≈ a[:, 1:n1]
-                @test q*b[1:n1] ≈ truncatedQ(q)*b[1:n1] atol=100ε
+                @test q*b[1:n1] ≈ rectangularQ(q)*b[1:n1] atol=100ε
                 @test q*b ≈ squareQ(q)*b atol=100ε
                 @test_throws DimensionMismatch q*b[1:n1 + 1]
                 @test_throws DimensionMismatch b[1:n1 + 1]*q'
@@ -163,7 +163,7 @@ end
 
 @testset "Issue 7304" begin
     A = [-√.5 -√.5; -√.5 √.5]
-    Q = truncatedQ(qrfact(A)[:Q])
+    Q = rectangularQ(qrfact(A)[:Q])
     @test vecnorm(A-Q) < eps()
 end