Question

Show $A$ has an $LU$ factorization if and only if for each $k$ with $ 1 \leq k \leq m$, the upper left block $A(1:k,1:k)$ is nonsingular.

score 1.7k · Answer 1 · 2026-05-10 15:56:28

1.7k

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Show $A$ has an $LU$ factorization if and only if for each $k$ with $ 1 \leq k \leq m$, the upper left block $A(1:k,1:k)$ is nonsingular.

Published on 10 May 2026 - 15:56

score 515 · Answer 2 · 2026-04-09 22:17:10

515

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What can we say about $A$ if $AA^T$ is singular?

Published on 09 Apr 2026 - 22:17

score 58 · Answer 3 · 2026-04-15 03:43:55

58

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matrix decomposition with SVD

Published on 15 Apr 2026 - 3:43

score 172 · Answer 4 · 2026-04-15 09:05:52

172

Views

Show that $\log(\det(H_1)) ≤ \log(\det(H_2)) + \operatorname{tr}[H^{-1}_2H_1]−N$ for all positive semidefinite matrices $H_1,H_2 \in C^N$

Published on 15 Apr 2026 - 9:05

score 751 · Answer 5 · 2026-05-10 17:16:51

751

Views

Are there any cases where Modified Gram-Schmidt is more reliable than Householder for QR decomposition?

Published on 10 May 2026 - 17:16

score 406 · Answer 6 · 2026-05-10 15:51:31

406

Views

Nearest Kronecker Product with Positive Semi-Definite Residual

Published on 10 May 2026 - 15:51

score 258 · Answer 7 · 2026-04-12 01:08:05

258

Views

Show that all eigenvalues of this pentadiagonal matrix are double degenerate

Published on 12 Apr 2026 - 1:08

score 1.7k · Answer 8 · 2026-05-07 14:14:23

1.7k

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Cost of LU decomposition (time cost)

Published on 07 May 2026 - 14:14

score 216 · Answer 9 · 2026-03-25 12:53:48

216

Views

Generate approximately semi-orthogonal tall matrix approximately satisfying constraints

Published on 25 Mar 2026 - 12:53

score 65 · Answer 10 · 2026-05-10 15:52:33

65

Views

How to find the inverse of $A\otimes A + (I+D\otimes D)^{-1}(D\otimes D)$ without forming the Kronecker product?

Published on 10 May 2026 - 15:52

score 213 · Answer 11 · 2026-05-10 15:52:35

213

Views

How to find the spectral decomposition of $A\otimes A + B\otimes B$ without forming the Kronecker product?

Published on 10 May 2026 - 15:52

score 2.2k · Answer 12 · 2026-04-14 09:58:59

2.2k

Views

How rank-revealing QR factorization determine the rank of the matrix?

Published on 14 Apr 2026 - 9:58

score 33 · Answer 13 · 2026-04-10 17:19:58

33

Views

How do you know what a matrix represents in matrix decomposition?

Published on 10 Apr 2026 - 17:19

score 402 · Answer 14 · 2026-05-10 10:06:59

402

Views

Could this possibly be a new simple proof for Schur's triangularization theorem?

Published on 10 May 2026 - 10:06

score 2.2k · Answer 15 · 2026-04-29 12:26:16

2.2k

Views

Why (which advantages) we use different matrix factorization algorithms?

Published on 29 Apr 2026 - 12:26

List Question

Show $A$ has an $LU$ factorization if and only if for each $k$ with $ 1 \leq k \leq m$, the upper left block $A(1:k,1:k)$ is nonsingular.

What can we say about $A$ if $AA^T$ is singular?

matrix decomposition with SVD

Show that $\log(\det(H_1)) ≤ \log(\det(H_2)) + \operatorname{tr}[H^{-1}_2H_1]−N$ for all positive semidefinite matrices $H_1,H_2 \in C^N$

Are there any cases where Modified Gram-Schmidt is more reliable than Householder for QR decomposition?

Nearest Kronecker Product with Positive Semi-Definite Residual

Show that all eigenvalues of this pentadiagonal matrix are double degenerate

Cost of LU decomposition (time cost)

Generate approximately semi-orthogonal tall matrix approximately satisfying constraints

How to find the inverse of $A\otimes A + (I+D\otimes D)^{-1}(D\otimes D)$ without forming the Kronecker product?

How to find the spectral decomposition of $A\otimes A + B\otimes B$ without forming the Kronecker product?

How rank-revealing QR factorization determine the rank of the matrix?

How do you know what a matrix represents in matrix decomposition?

Could this possibly be a new simple proof for Schur's triangularization theorem?

Why (which advantages) we use different matrix factorization algorithms?

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