List questions from matrix-decomposition

Published on 02 Oct 2020 - 21:14

261

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Is the polar decomposition of a product the product of polar decompositions?

Published on 03 Oct 2020 - 17:11

1.2k

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Why normalize the eigenvectors when computing SVD and what happens if you do not normalize the eigenvectors?

Published on 31 Mar 2026 - 21:48

137

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Finding good bases to represent any rectangular matrix as a block matrix with identity submatrix

Published on 05 Apr 2026 - 17:00

1.6k

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SVD - Linking right and left singular vectors

Published on 31 Mar 2026 - 21:48

82

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How to construct the corner of a positive-definite matrix

Published on 09 Oct 2020 - 22:06

43

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Diagonal-preserving low-rank approximation

Published on 10 Oct 2020 - 9:33

24

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given a symmetric matrix $A_{n\times n}$ and integer $m$, is there any matrix $X_{n\times m}$, s.t., $X\times X^{t}=A$?

Published on 29 Mar 2026 - 23:47

712

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Finding eigenvalues and eigenvectors after SVD?

Published on 31 Mar 2026 - 21:54

242

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Uniqueness of QR decomposition of rank n-1 matrix

Published on 04 Apr 2026 - 5:21

38

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Orthogonality in QR Decomposition

Published on 13 Oct 2020 - 1:07

681

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Singular value decomposition of a $3\times 1$ matrix

Published on 31 Mar 2026 - 21:50

415

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Prove that if $A^{t}A$ is idempotent then $A^{t}=A^{+}$

Published on 18 Oct 2020 - 13:20

359

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Solving for a matrix polynomial

Published on 19 Oct 2020 - 7:18

119

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Why do we need to store $2np-p^2$ entries and not $mp+np$ entries for a rank $p$ matrix?

Published on 04 Apr 2026 - 5:21

List Question

Matrix Eigenvalue Problem

Is the polar decomposition of a product the product of polar decompositions?

Why normalize the eigenvectors when computing SVD and what happens if you do not normalize the eigenvectors?

Finding good bases to represent any rectangular matrix as a block matrix with identity submatrix

SVD - Linking right and left singular vectors

How to construct the corner of a positive-definite matrix

Diagonal-preserving low-rank approximation

given a symmetric matrix $A_{n\times n}$ and integer $m$, is there any matrix $X_{n\times m}$, s.t., $X\times X^{t}=A$?

Finding eigenvalues and eigenvectors after SVD?

Uniqueness of QR decomposition of rank n-1 matrix

Orthogonality in QR Decomposition

Singular value decomposition of a $3\times 1$ matrix

Prove that if $A^{t}A$ is idempotent then $A^{t}=A^{+}$

Solving for a matrix polynomial

Why do we need to store $2np-p^2$ entries and not $mp+np$ entries for a rank $p$ matrix?

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