Question

Unique decomposition of a positive definite matrix into a sum of outer products ${\bf x}_k{\bf x}_k^{\rm T}$ and a diagonal matrix?

score 2.2k · Answer 1 · 2017-01-05 02:38:09

2.2k

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Unique decomposition of a positive definite matrix into a sum of outer products ${\bf x}_k{\bf x}_k^{\rm T}$ and a diagonal matrix?

Published on 05 Jan 2017 - 2:38

score 7.9k · Answer 2 · 2026-03-27 06:06:22

7.9k

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Singularity positive semidefinite

Published on 27 Mar 2026 - 6:06

score 2.5k · Answer 3 · 2017-01-07 11:23:06

2.5k

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How to prove that $\det(A+B) ≥ \det A +\det B$?

Published on 07 Jan 2017 - 11:23

score 641 · Answer 4 · 2017-01-09 02:56:17

641

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How to prove the positive-definiteness of this matrix?

Published on 09 Jan 2017 - 2:56

score 43 · Answer 5 · 2017-01-10 04:06:46

43

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A question about positive definite and symmetric matrices

Published on 10 Jan 2017 - 4:06

score 754 · Answer 6 · 2017-01-14 21:10:47

754

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Positive definiteness of matrix A.

Published on 14 Jan 2017 - 21:10

score 38 · Answer 7 · 2017-01-17 11:54:53

38

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Eigenvalues of "$A^{1/2}B^{-1}A^{1/2}$" equal to 1

Published on 17 Jan 2017 - 11:54

score 303 · Answer 8 · 2026-03-27 06:08:54

303

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Given $P$ a real symmetric positive semidefinite matrix, what matrix $A$ ensure that $A^TPA$ is PSD?

Published on 27 Mar 2026 - 6:08

score 65 · Answer 9 · 2017-01-19 06:21:50

65

Views

Uniqueness of automorphisms $\theta$ and $\psi$ in polar decomposition of $\alpha=\psi\theta$

Published on 19 Jan 2017 - 6:21

score 176 · Answer 10 · 2017-01-20 22:48:04

176

Views

Show that $10x^2+30y^2-4xy > 0$ when $x,y$ are not both zero

Published on 20 Jan 2017 - 22:48

score 74 · Answer 11 · 2026-03-28 00:31:01

74

Views

Showing that $c:=\min\{\frac{\|\alpha(v)\|}{\|v\|}:0\neq v\in Ker(\alpha)^{\perp}\}$ is a singular value of $\alpha$

Published on 28 Mar 2026 - 0:31

score 81 · Answer 12 · 2017-02-03 02:02:13

81

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Possible Positive-definite matrix question

Published on 03 Feb 2017 - 2:02

score 69 · Answer 13 · 2017-02-06 18:50:57

69

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Showing that $D^{-1}- A'( A D A')^{-1} A$ is positive semi-definite

Published on 06 Feb 2017 - 18:50

score 35 · Answer 14 · 2026-03-28 03:02:21

35

Views

$G\Sigma G'=\Sigma$ for all orthonormal matrices $G$

Published on 28 Mar 2026 - 3:02

score 338 · Answer 15 · 2026-03-25 11:26:28

338

Views

Linear kernel is strictly positive definite, but corresponding RKHS in not dense in C(R)?

Published on 25 Mar 2026 - 11:26

List Question

Unique decomposition of a positive definite matrix into a sum of outer products ${\bf x}_k{\bf x}_k^{\rm T}$ and a diagonal matrix?

Singularity positive semidefinite

How to prove that $\det(A+B) ≥ \det A +\det B$?

How to prove the positive-definiteness of this matrix?

A question about positive definite and symmetric matrices

Positive definiteness of matrix A.

Eigenvalues of "$A^{1/2}B^{-1}A^{1/2}$" equal to 1

Given $P$ a real symmetric positive semidefinite matrix, what matrix $A$ ensure that $A^TPA$ is PSD?

Uniqueness of automorphisms $\theta$ and $\psi$ in polar decomposition of $\alpha=\psi\theta$

Show that $10x^2+30y^2-4xy > 0$ when $x,y$ are not both zero

Showing that $c:=\min\{\frac{\|\alpha(v)\|}{\|v\|}:0\neq v\in Ker(\alpha)^{\perp}\}$ is a singular value of $\alpha$

Possible Positive-definite matrix question

Showing that $D^{-1}- A'( A D A')^{-1} A$ is positive semi-definite

$G\Sigma G'=\Sigma$ for all orthonormal matrices $G$

Linear kernel is strictly positive definite, but corresponding RKHS in not dense in C(R)?

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