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[de] cs-229-linear-algebra #136
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Hi @bb08, thank you again for all your work! Would you know someone who could take a look at your translation? After the review phase, we can merge your translation to the repository. |
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some tweaks (precision and minor spelling corrections) on a - in general - high quality translation
de/refresher-linear-algebra.md
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**15. inner product: for x,y∈Rn, we have:** | ||
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⟶ Innere Produkt: Auch Skalarprodukt, Es gilt x,y∈Rn:** |
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⟶ inneres Produkt: auch Skalarprodukt, Es gilt x,y∈Rn:**
de/refresher-linear-algebra.md
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**26. Trace ― The trace of a square matrix A, noted tr(A), is the sum of its diagonal entries:** | ||
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⟶ Spur - Die Spurabbildung einer quadratischen Matrix A, geschrieben als tr(A), ist die summe der Diagonaleinheiten: |
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⟶ Spur - Die Spurabbildung (Spurfunktion) einer quadratischen Matrix A, geschrieben als tr(A), ist die Summe der Diagonaleinheiten:
de/refresher-linear-algebra.md
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**29. Remark: A is invertible if and only if |A|≠0. Also, |AB|=|A||B| and |AT|=|A|.** | ||
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⟶ Wichtig: A ist nur invertierbar falls |A|≠0. Weiteres gilt |AB|=|A||B| and |AT|=|A| |
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⟶ Wichtig: A ist nur invertierbar, falls |A|≠0. Des Weiteren gilt |AB|=|A||B| and |AT|=|A|
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**43. Remark: similarly, a matrix A is said to be positive definite, and is noted A≻0, if it is a PSD matrix which satisfies for all non-zero vector x, xTAx>0.** | ||
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⟶ Wichtig: Ebenfalls gilt, Eine Matrix A ist positiv definit, A≻0, falls diese eine PSD Matrix ist und es gilt für alle Einheiten eines Vektors x ungleich 0: x, xTAx>0. |
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⟶ Wichtig: Ebenfalls gilt, dass eine Matrix A positiv definit ist, in der Notatition: A≻0, falls diese eine PSD Matrix ist und es gilt für alle Einheiten eines Vektors x ungleich 0: x, xTAx>0.
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**44. Eigenvalue, eigenvector ― Given a matrix A∈Rn×n, λ is said to be an eigenvalue of A if there exists a vector z∈Rn∖{0}, called eigenvector, such that we have:** | ||
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⟶ Eigenwert, Eigenvektor - Sei A∈Rn×n eine Matrix und λ der Eigentwert von A, falls es einen Vektor z∈Rn∖{0} gibt, Eigentvektor genannt, gilt folgendes: |
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⟶ Eigenwert, Eigenvektor - Sei A∈Rn×n eine Matrix und λ der Eigenwert von A, falls es einen Vektor z∈Rn∖{0}, Eigenvektor genannt, gibt. Dann gilt:
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**45. Spectral theorem ― Let A∈Rn×n. If A is symmetric, then A is diagonalizable by a real orthogonal matrix U∈Rn×n. By noting Λ=diag(λ1,...,λn), we have:** | ||
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⟶ Spektralsatz - Sei A∈Rn×n, falls A eine symmetrische Matrix, dann ist diese diagonalisierbar durch eine orthogonale Matrix U∈Rn×n. Durch Λ=diag(λ1,...,λn) gilt folgendes: |
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⟶ Spektralsatz - Sei A∈Rn×n, falls A eine symmetrische Matrix, dann ist diese diagonalisierbar durch eine orthogonale Matrix U∈Rn×n. Mit der Notation Λ=diag(λ1,...,λn) gilt folgendes:
Hey! Done, I added @dee1337 suggestions |
Hey! German natives welcome, happy to have some discussion and corrections about the translation
Cheers