Question

Quadratic form with positive semi-definite matrix

score 49 · Answer 1 · 2026-03-28 07:58:48

49

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Quadratic form with positive semi-definite matrix

Published on 28 Mar 2026 - 7:58

score 28 · Answer 2 · 2024-02-21 11:08:31

28

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For an $n$ by $n$ symmetric matrix $M$, why does $Tr(M)^2/Tr(M^2)>n-1$ imply that M is positive or negative definite?

Published on 21 Feb 2024 - 11:08

score 35 · Answer 3 · 2026-03-26 11:03:35

35

Views

$0 ≤ A ≤ I. $ $\iff$ ⟨ψ|A|ψ⟩ ∈ [0, 1] for every unit vector $|ψ⟩ ∈ H$

Published on 26 Mar 2026 - 11:03

score 44 · Answer 4 · 2026-03-27 03:59:52

44

Views

Sum of norms induced by PSD matrices

Published on 27 Mar 2026 - 3:59

score 71 · Answer 5 · 2024-02-25 21:51:04

71

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If $A$ is a symmetric positive definite matrix, show that $f(x) = x^TAx$ is convex.

Published on 25 Feb 2024 - 21:51

score 14 · Answer 6 · 2026-03-02 10:23:43

14

Views

Factorizing $AMA^T+N=WW^T$ efficiently.

Published on 02 Mar 2026 - 10:23

score 23 · Answer 7 · 2026-03-28 09:50:26

23

Views

how to show that a nonsingular positive semidefinite matrix is positive definite?

Published on 28 Mar 2026 - 9:50

score 25 · Answer 8 · 2026-03-28 09:50:18

25

Views

Sum of positive semi-definite matrix and positive definite matrix?

Published on 28 Mar 2026 - 9:50

score 47 · Answer 9 · 2024-03-06 17:33:07

47

Views

Given matrix A with $A_{i,j} = f(i,j)$, how can I find out if A is positive semidefinite?

Published on 06 Mar 2024 - 17:33

score 19 · Answer 10 · 2024-03-06 18:15:06

19

Views

Positive Matrices and Linear Forms

Published on 06 Mar 2024 - 18:15

score 11 · Answer 11 · 2024-03-10 19:05:32

11

Views

Infer the positive definiteness of a real non-symmetric matrix from the positive definiteness of its symmetric part

Published on 10 Mar 2024 - 19:05

score 23 · Answer 12 · 2026-03-25 10:57:21

23

Views

For a fixed positive definite $A$, is $(x,B) \to x^TB^{-1/2} A B^{-1/2} x$ always jointly convex?

Published on 25 Mar 2026 - 10:57

score 25 · Answer 13 · 2024-03-11 17:29:25

25

Views

Show in terms of numerics for symmetric and positive definite matrix

Published on 11 Mar 2024 - 17:29

score 15 · Answer 14 · 2026-02-24 15:27:27

15

Views

Show that to reduce the initial error by the factor $\varepsilon$ at most many iteration steps are required

Published on 24 Feb 2026 - 15:27

score 45 · Answer 15 · 2024-03-18 04:28:02

45

Views

Would $v^TAv>0$ forall $v$, $v$ if A's eigenvalues are all > 0?

Published on 18 Mar 2024 - 4:28

List Question

Quadratic form with positive semi-definite matrix

For an $n$ by $n$ symmetric matrix $M$, why does $Tr(M)^2/Tr(M^2)>n-1$ imply that M is positive or negative definite?

$0 ≤ A ≤ I. $ $\iff$ ⟨ψ|A|ψ⟩ ∈ [0, 1] for every unit vector $|ψ⟩ ∈ H$

Sum of norms induced by PSD matrices

If $A$ is a symmetric positive definite matrix, show that $f(x) = x^TAx$ is convex.

Factorizing $AMA^T+N=WW^T$ efficiently.

how to show that a nonsingular positive semidefinite matrix is positive definite?

Sum of positive semi-definite matrix and positive definite matrix?

Given matrix A with $A_{i,j} = f(i,j)$, how can I find out if A is positive semidefinite?

Positive Matrices and Linear Forms

Infer the positive definiteness of a real non-symmetric matrix from the positive definiteness of its symmetric part

For a fixed positive definite $A$, is $(x,B) \to x^TB^{-1/2} A B^{-1/2} x$ always jointly convex?

Show in terms of numerics for symmetric and positive definite matrix

Show that to reduce the initial error by the factor $\varepsilon$ at most many iteration steps are required

Would $v^TAv>0$ forall $v$, $v$ if A's eigenvalues are all > 0?

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