Question

minimize the trace of a matrix function

score 373 · Answer 1 · 2020-06-13 07:23:55

373

Views

minimize the trace of a matrix function

Published on 13 Jun 2020 - 7:23

score 330 · Answer 2 · 2026-03-25 08:07:10

330

Views

Generating symmetric Positive Definite Matrix from random vector multiplication yield singular matrix

Published on 25 Mar 2026 - 8:07

score 156 · Answer 3 · 2020-06-18 10:08:45

156

Views

An expression subtly different from the one in Sherman-Morrison formula

Published on 18 Jun 2020 - 10:08

score 102 · Answer 4 · 2020-06-18 14:17:32

102

Views

Outer normal of the set positive definite matrices as a subset of symmetric matrices

Published on 18 Jun 2020 - 14:17

score 66 · Answer 5 · 2026-03-25 23:42:45

66

Views

If $T$ is self-adjoint and $\langle T(u),u \rangle > 0$ for every $u$ in $K$, $u\neq0$ then $T = R^2$ for some self-adjoint non-singular operator $R$

Published on 25 Mar 2026 - 23:42

score 352 · Answer 6 · 2020-06-20 22:40:15

352

Views

Etymology of the term "positive definite"

Published on 20 Jun 2020 - 22:40

score 38 · Answer 7 · 2026-03-27 14:03:25

38

Views

Given positive definite $X\in\mathbb{R}^{4\times 4}$, find $Y\in\mathbb{R}^{4\times 2}$, such that $YY'\approx X$

Published on 27 Mar 2026 - 14:03

score 501 · Answer 8 · 2020-06-23 17:31:16

501

Views

Show that the matrix $B$ is positive definite without using the positive pivot and determinant test.

Published on 23 Jun 2020 - 17:31

score 81 · Answer 9 · 2026-03-26 10:58:11

81

Views

When is $v^T A w > 0$?

Published on 26 Mar 2026 - 10:58

score 306 · Answer 10 · 2020-06-25 14:35:27

306

Views

Under what conditions is $A^T \Sigma A$ positive (semi-)definite for $\Sigma$ p.s.d?

Published on 25 Jun 2020 - 14:35

score 414 · Answer 11 · 2026-03-25 11:08:37

414

Views

Eigenvector problem with ellipsoids (maximizing quadratic form)

Published on 25 Mar 2026 - 11:08

score 81 · Answer 12 · 2020-06-26 11:25:29

81

Views

Is $x^T (\sum_{i} e^{\lambda_i} A_i)^{-1} x + \ln \det \sum_{i} e^{\lambda_i} A_i $ a convex function in $\lambda$, where $A_i$ p.d.?

Published on 26 Jun 2020 - 11:25

score 111 · Answer 13 · 2020-06-28 17:30:36

111

Views

Show that $A=(a_{ij})_{1\le i,j\le5}$ is positive definite, where $a_{ij}=\frac1{n_i+n_j+1}$

Published on 28 Jun 2020 - 17:30

score 178 · Answer 14 · 2020-06-29 15:56:34

178

Views

Can every symmetric, unimodular and positive definite $G\in\mathbb{Z}^{n\times n}$ be written as $G=U^TU$?

Published on 29 Jun 2020 - 15:56

score 41 · Answer 15 · 2020-07-02 09:55:12

41

Views

Prove that $LL^T$ is PD

Published on 02 Jul 2020 - 9:55

List Question

minimize the trace of a matrix function

Generating symmetric Positive Definite Matrix from random vector multiplication yield singular matrix

An expression subtly different from the one in Sherman-Morrison formula

Outer normal of the set positive definite matrices as a subset of symmetric matrices

If $T$ is self-adjoint and $\langle T(u),u \rangle > 0$ for every $u$ in $K$, $u\neq0$ then $T = R^2$ for some self-adjoint non-singular operator $R$

Etymology of the term "positive definite"

Given positive definite $X\in\mathbb{R}^{4\times 4}$, find $Y\in\mathbb{R}^{4\times 2}$, such that $YY'\approx X$

Show that the matrix $B$ is positive definite without using the positive pivot and determinant test.

When is $v^T A w > 0$?

Under what conditions is $A^T \Sigma A$ positive (semi-)definite for $\Sigma$ p.s.d?

Eigenvector problem with ellipsoids (maximizing quadratic form)

Is $x^T (\sum_{i} e^{\lambda_i} A_i)^{-1} x + \ln \det \sum_{i} e^{\lambda_i} A_i $ a convex function in $\lambda$, where $A_i$ p.d.?

Show that $A=(a_{ij})_{1\le i,j\le5}$ is positive definite, where $a_{ij}=\frac1{n_i+n_j+1}$

Can every symmetric, unimodular and positive definite $G\in\mathbb{Z}^{n\times n}$ be written as $G=U^TU$?

Prove that $LL^T$ is PD

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