Question

(Proof Updated, Verification in Need) Show that $(s,t)\mapsto t\wedge s$ for $s,t\geq 0$ and $(s,t)\mapsto e^{-|t-s|}$ are positive semi-definite.

score 244 · Answer 1 · 2020-02-17 22:17:37

244

Views

(Proof Updated, Verification in Need) Show that $(s,t)\mapsto t\wedge s$ for $s,t\geq 0$ and $(s,t)\mapsto e^{-|t-s|}$ are positive semi-definite.

Published on 17 Feb 2020 - 22:17

score 208 · Answer 2 · 2026-03-25 06:30:19

208

Views

How to prove the $n\times n$ matrix $A=\big(\frac{1}{i+j+1}\big)_{i,j\in [n]}$ is positive semi-definite?

Published on 25 Mar 2026 - 6:30

score 92 · Answer 3 · 2020-02-23 06:12:21

92

Views

Positive semi-definiteness of the difference between oblique and orthogonal projections

Published on 23 Feb 2020 - 6:12

score 60 · Answer 4 · 2020-02-23 08:18:51

60

Views

2-norm of product of multiple matrices

Published on 23 Feb 2020 - 8:18

score 114 · Answer 5 · 2026-03-25 06:29:32

114

Views

When applying semidefinite optimization to sum of squares polynomials, why do you want the determinant of you polynomial matrix to be non-negative?

Published on 25 Mar 2026 - 6:29

score 58 · Answer 6 · 2020-02-25 18:37:30

58

Views

Why is it insufficient to say that a symmetric matrix A is positive semidefinite if it has non-negative diagonals?

Published on 25 Feb 2020 - 18:37

score 128 · Answer 7 · 2020-02-25 19:42:29

128

Views

How to show that this matrix is positive semi-definite?

Published on 25 Feb 2020 - 19:42

score 245 · Answer 8 · 2020-02-25 20:23:26

245

Views

How to show this matrix is diagonally dominant

Published on 25 Feb 2020 - 20:23

score 422 · Answer 9 · 2020-02-25 21:11:12

422

Views

Positive-definiteness of matrix with $|a_{ij}| \leq \frac{1}{ij}$

Published on 25 Feb 2020 - 21:11

score 1.3k · Answer 10 · 2020-02-26 07:39:38

1.3k

Views

Principal minors and semi-definiteness

Published on 26 Feb 2020 - 7:39

score 27 · Answer 11 · 2026-03-25 06:30:47

27

Views

Why is a matrix $Z = (<u_iu_i^T,u_ju_j^T>)_{i,j\in [n+1]}$ with $\{u_i\}_{i\in[n]}$ orthonormal representation of a graph positive semi-definite?

Published on 25 Mar 2026 - 6:30

score 256 · Answer 12 · 2020-02-29 13:28:41

256

Views

Positive-definiteness of matrix with $0 \leq a_{ij} \leq \frac{1}{ij}$

Published on 29 Feb 2020 - 13:28

score 144 · Answer 13 · 2026-03-25 08:08:35

144

Views

Characterization of Graph Laplacians

Published on 25 Mar 2026 - 8:08

score 251 · Answer 14 · 2026-03-25 06:30:21

251

Views

Prove that $X$ is PSD $\iff$ the principal submatrix of $X$ with all maximally linearly independent columns (and corresponding rows) left is PD.

Published on 25 Mar 2026 - 6:30

score 52 · Answer 15 · 2020-03-06 14:19:01

52

Views

A positive-semidefinite polynomial

Published on 06 Mar 2020 - 14:19

List Question

(Proof Updated, Verification in Need) Show that $(s,t)\mapsto t\wedge s$ for $s,t\geq 0$ and $(s,t)\mapsto e^{-|t-s|}$ are positive semi-definite.

How to prove the $n\times n$ matrix $A=\big(\frac{1}{i+j+1}\big)_{i,j\in [n]}$ is positive semi-definite?

Positive semi-definiteness of the difference between oblique and orthogonal projections

2-norm of product of multiple matrices

When applying semidefinite optimization to sum of squares polynomials, why do you want the determinant of you polynomial matrix to be non-negative?

Why is it insufficient to say that a symmetric matrix A is positive semidefinite if it has non-negative diagonals?

How to show that this matrix is positive semi-definite?

How to show this matrix is diagonally dominant

Positive-definiteness of matrix with $|a_{ij}| \leq \frac{1}{ij}$

Principal minors and semi-definiteness

Why is a matrix $Z = (<u_iu_i^T,u_ju_j^T>)_{i,j\in [n+1]}$ with $\{u_i\}_{i\in[n]}$ orthonormal representation of a graph positive semi-definite?

Positive-definiteness of matrix with $0 \leq a_{ij} \leq \frac{1}{ij}$

Characterization of Graph Laplacians

Prove that $X$ is PSD $\iff$ the principal submatrix of $X$ with all maximally linearly independent columns (and corresponding rows) left is PD.

A positive-semidefinite polynomial

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