Question

A real-valued$\Rightarrow$Matrix $S$ of Cholesky-decomposition $A=SS^T$ is real valued.

score 241 · Answer 1 · 2026-03-27 04:00:04

241

Views

A real-valued$\Rightarrow$Matrix $S$ of Cholesky-decomposition $A=SS^T$ is real valued.

Published on 27 Mar 2026 - 4:00

score 58 · Answer 2 · 2019-12-13 12:28:31

58

Views

Is there a special name for the upper triangular matrix $R$ obtained from LR/QR/Cholesky-decomposition?

Published on 13 Dec 2019 - 12:28

score 53 · Answer 3 · 2019-12-18 19:32:50

53

Views

Show that there exists $Y \in \mathbb{C}^n$ such that $P$ is the characteristic polynomial of $A+XY^{T}$

Published on 18 Dec 2019 - 19:32

score 273 · Answer 4 · 2026-03-26 07:58:46

273

Views

if $A$ is a symmetric and nonnegative definite matrix then $A=LL^T$ for some $L$ lower triangular matrix.

Published on 26 Mar 2026 - 7:58

score 236 · Answer 5 · 2019-12-22 01:54:09

236

Views

Determine linear combination of rank 1 matrices for a rank 2 matrix?

Published on 22 Dec 2019 - 1:54

score 498 · Answer 6 · 2019-12-23 17:16:07

498

Views

For $QR$ decomposition, does R always have to be upper triangular matrix?

Published on 23 Dec 2019 - 17:16

score 957 · Answer 7 · 2019-12-24 10:47:02

957

Views

How can QR-decomposition be used for low-rank estimation?

Published on 24 Dec 2019 - 10:47

score 29 · Answer 8 · 2026-03-27 00:03:44

29

Views

Geometric interpretation of $\Sigma^{-1}\Phi x$ where $\Phi = [\phi_1,\phi_2,\cdots, \phi_n]$, $\Sigma=\sum_{i=1}^{n} \phi_i\phi_i^T+\lambda I$

Published on 27 Mar 2026 - 0:03

score 43 · Answer 9 · 2026-03-25 04:55:34

43

Views

Factoring matrices over $\mathbb{Z}_k$ for $k$ composite?

Published on 25 Mar 2026 - 4:55

score 960 · Answer 10 · 2026-03-26 22:57:53

960

Views

How to show the relationship between the eigenvector of $A^TA$ and $AA^T$?

Published on 26 Mar 2026 - 22:57

score 45 · Answer 11 · 2020-01-09 11:46:51

45

Views

Adding the column space of a matrix with another matrix?

Published on 09 Jan 2020 - 11:46

score 83 · Answer 12 · 2026-03-26 09:40:03

83

Views

Find matrix $B$ such that $B B^\top \approx A$

Published on 26 Mar 2026 - 9:40

score 31 · Answer 13 · 2020-01-09 21:46:19

31

Views

Uniqueness of $\rho = AA^*$.

Published on 09 Jan 2020 - 21:46

score 140 · Answer 14 · 2020-01-10 14:15:10

140

Views

LU decomposition of invertible matrix

Published on 10 Jan 2020 - 14:15

score 201 · Answer 15 · 2020-01-11 17:03:35

201

Views

Let $A$ be a $10\times 10$ matrix and $A^{10,000} = 0$ Show $A^{10} = 0$

Published on 11 Jan 2020 - 17:03

List Question

A real-valued$\Rightarrow$Matrix $S$ of Cholesky-decomposition $A=SS^T$ is real valued.

Is there a special name for the upper triangular matrix $R$ obtained from LR/QR/Cholesky-decomposition?

Show that there exists $Y \in \mathbb{C}^n$ such that $P$ is the characteristic polynomial of $A+XY^{T}$

if $A$ is a symmetric and nonnegative definite matrix then $A=LL^T$ for some $L$ lower triangular matrix.

Determine linear combination of rank 1 matrices for a rank 2 matrix?

For $QR$ decomposition, does R always have to be upper triangular matrix?

How can QR-decomposition be used for low-rank estimation?

Geometric interpretation of $\Sigma^{-1}\Phi x$ where $\Phi = [\phi_1,\phi_2,\cdots, \phi_n]$, $\Sigma=\sum_{i=1}^{n} \phi_i\phi_i^T+\lambda I$

Factoring matrices over $\mathbb{Z}_k$ for $k$ composite?

How to show the relationship between the eigenvector of $A^TA$ and $AA^T$?

Adding the column space of a matrix with another matrix?

Find matrix $B$ such that $B B^\top \approx A$

Uniqueness of $\rho = AA^*$.

LU decomposition of invertible matrix

Let $A$ be a $10\times 10$ matrix and $A^{10,000} = 0$ Show $A^{10} = 0$

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