Question

How to judge a special matrix is a positive-definite-matrix

score 267 · Answer 1 · 2013-05-06 08:53:54

267

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How to judge a special matrix is a positive-definite-matrix

Published on 06 May 2013 - 8:53

score 4.2k · Answer 2 · 2026-03-25 15:43:49

4.2k

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Properties of the cone of positive semidefinite matrices

Published on 25 Mar 2026 - 15:43

score 1.9k · Answer 3 · 2013-05-10 07:55:22

1.9k

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When is $\det(A+B)=\det(A)+\det(B)$ for positive definite $A$ and positive semidefinite $B$?

Published on 10 May 2013 - 7:55

score 8k · Answer 4 · 2026-03-25 12:48:40

8k

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Cholesky decomposition in positive semi-definite matrix

Published on 25 Mar 2026 - 12:48

score 1.7k · Answer 5 · 2026-03-26 09:41:52

1.7k

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How is the rank of $A$ related to the characteristic polynomial of the adjugate matrix of $A$?

Published on 26 Mar 2026 - 9:41

score 1k · Answer 6 · 2013-08-14 17:17:27

1k

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Show that if $A$ is positive definite then $A + A^{-1} - 2I$ is positive semidefinite

Published on 14 Aug 2013 - 17:17

score 2k · Answer 7 · 2013-08-22 20:37:58

2k

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Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$

Published on 22 Aug 2013 - 20:37

score 17.2k · Answer 8 · 2013-09-03 03:22:43

17.2k

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A matrix is positive semidefinite iff it can be written in the form $X'X$

Published on 03 Sep 2013 - 3:22

score 6.1k · Answer 9 · 2013-09-30 20:25:30

6.1k

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Criterion for positive semidefinite matrices

Published on 30 Sep 2013 - 20:25

score 5.3k · Answer 10 · 2013-10-06 12:53:34

5.3k

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Why do mathematicians use only symmetric matrices when they want positive semi-definite matrices?

Published on 06 Oct 2013 - 12:53

score 61.1k · Answer 11 · 2013-10-08 13:00:29

61.1k

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Prove that every positive semidefinite matrix has nonnegative eigenvalues

Published on 08 Oct 2013 - 13:00

score 3.6k · Answer 12 · 2026-03-25 08:12:56

3.6k

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How to project a symmetric matrix onto the cone of positive semidefinite (PSD) matrices?

Published on 25 Mar 2026 - 8:12

score 2.1k · Answer 13 · 2014-01-28 14:28:58

2.1k

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Is the product of $3$ positive semidefinite matrices positive semidefinite?

Published on 28 Jan 2014 - 14:28

score 2.9k · Answer 14 · 2014-02-10 14:23:57

2.9k

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Product of symmetric positive definite matrices

Published on 10 Feb 2014 - 14:23

score 2.3k · Answer 15 · 2014-02-16 18:14:53

2.3k

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Positive semidefinite cone is generated by all rank-$1$ matrices.

Published on 16 Feb 2014 - 18:14

List Question

How to judge a special matrix is a positive-definite-matrix

Properties of the cone of positive semidefinite matrices

When is $\det(A+B)=\det(A)+\det(B)$ for positive definite $A$ and positive semidefinite $B$?

Cholesky decomposition in positive semi-definite matrix

How is the rank of $A$ related to the characteristic polynomial of the adjugate matrix of $A$?

Show that if $A$ is positive definite then $A + A^{-1} - 2I$ is positive semidefinite

Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$

A matrix is positive semidefinite iff it can be written in the form $X'X$

Criterion for positive semidefinite matrices

Why do mathematicians use only symmetric matrices when they want positive semi-definite matrices?

Prove that every positive semidefinite matrix has nonnegative eigenvalues

How to project a symmetric matrix onto the cone of positive semidefinite (PSD) matrices?

Is the product of $3$ positive semidefinite matrices positive semidefinite?

Product of symmetric positive definite matrices

Positive semidefinite cone is generated by all rank-$1$ matrices.

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