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 · 2026-03-25 07:46:00

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 25 Mar 2026 - 7:46

score 512 · Answer 2 · 2018-06-14 16:46:50

512

Views

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

Published on 14 Jun 2018 - 16:46

score 55 · Answer 3 · 2018-06-15 03:08:54

55

Views

matrix decomposition with SVD

Published on 15 Jun 2018 - 3:08

score 170 · Answer 4 · 2018-06-15 11:46:47

170

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 Jun 2018 - 11:46

score 750 · Answer 5 · 2026-03-24 23:48:14

750

Views

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

Published on 24 Mar 2026 - 23:48

score 401 · Answer 6 · 2026-03-25 01:16:21

401

Views

Nearest Kronecker Product with Positive Semi-Definite Residual

Published on 25 Mar 2026 - 1:16

score 255 · Answer 7 · 2018-06-20 14:27:59

255

Views

Show that all eigenvalues of this pentadiagonal matrix are double degenerate

Published on 20 Jun 2018 - 14:27

score 1.7k · Answer 8 · 2026-03-22 08:58:55

1.7k

Views

Cost of LU decomposition (time cost)

Published on 22 Mar 2026 - 8:58

score 215 · Answer 9 · 2026-03-23 22:35:15

215

Views

Generate approximately semi-orthogonal tall matrix approximately satisfying constraints

Published on 23 Mar 2026 - 22:35

score 60 · Answer 10 · 2026-03-25 03:04:19

60

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 25 Mar 2026 - 3:04

score 206 · Answer 11 · 2026-03-25 04:43:28

206

Views

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

Published on 25 Mar 2026 - 4:43

score 2.2k · Answer 12 · 2018-06-26 23:29:31

2.2k

Views

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

Published on 26 Jun 2018 - 23:29

score 30 · Answer 13 · 2018-06-27 21:53:36

30

Views

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

Published on 27 Jun 2018 - 21:53

score 393 · Answer 14 · 2026-03-24 23:53:51

393

Views

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

Published on 24 Mar 2026 - 23:53

score 2.2k · Answer 15 · 2026-03-21 22:51:55

2.2k

Views

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

Published on 21 Mar 2026 - 22:51

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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