List questions from positive-semidefinite

Published on 15 May 2020 - 21:48

151

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The norm $\|S-Q\|_F$ where $Q$ is orthogonal is minimised by $Q=I$

Published on 26 Mar 2026 - 4:36

60

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Would symmetry positive semi-definite matrix always decomposable?

Published on 26 May 2020 - 19:23

690

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For non-negative definite symmetric matrices, $\mathrm{tr}(AB)\le \mathrm{tr}(A)\mathrm{tr}(B)$

Published on 26 Mar 2026 - 4:30

56

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Prove or give a counterexample for semi positive defined matrices

Published on 27 May 2020 - 22:57

37

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Prove $\{X\in S^n_+ | \langle A,X \rangle =a, \langle B,X\rangle =b, \langle C,X\rangle =c\}$ is bounded

Published on 25 Mar 2026 - 11:32

316

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Positive semidefinite relations under square root operation

Published on 01 Jun 2020 - 23:40

482

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Proving "annihilator matrix "is positive semidefinite

Published on 03 Jun 2020 - 5:50

54

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Equivalence of semidefiniteness and quadratic inequality

Published on 05 Jun 2020 - 7:42

34

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How can we take use Cholesky factorization to show that a given symmetric matrix, M is positive semi-definite?

Published on 06 Jun 2020 - 13:34

329

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Hessian Matrix is positive semidefinite

Published on 13 Jun 2020 - 9:41

199

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Prove or disprove, if $A\in\mathbb R^{n×n}$ is positive semidefinite and symmetric then $\sqrt{A_{ii}A_{jj}}\ge |A_{ij}|$, $\forall 1\le i,j\le n$

Published on 14 Jun 2020 - 4:02

201

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If $\rho\leq\sigma$, is $\operatorname{rank}(\rho)\leq\operatorname{rank}(\sigma)$?

Published on 15 Jun 2020 - 22:29

790

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Prove that V is an identity operator

Published on 25 Mar 2026 - 15:58

188

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Relaxed Loewner-order inequalities for matrix modulus

Published on 18 Jun 2020 - 9:31

List Question

Proof of positive semi-definiteness of hat matrix product

The norm $\|S-Q\|_F$ where $Q$ is orthogonal is minimised by $Q=I$

Would symmetry positive semi-definite matrix always decomposable?

For non-negative definite symmetric matrices, $\mathrm{tr}(AB)\le \mathrm{tr}(A)\mathrm{tr}(B)$

Prove or give a counterexample for semi positive defined matrices

Prove $\{X\in S^n_+ | \langle A,X \rangle =a, \langle B,X\rangle =b, \langle C,X\rangle =c\}$ is bounded

Positive semidefinite relations under square root operation

Proving "annihilator matrix "is positive semidefinite

Equivalence of semidefiniteness and quadratic inequality

How can we take use Cholesky factorization to show that a given symmetric matrix, M is positive semi-definite?

Hessian Matrix is positive semidefinite

Prove or disprove, if $A\in\mathbb R^{n×n}$ is positive semidefinite and symmetric then $\sqrt{A_{ii}A_{jj}}\ge |A_{ij}|$, $\forall 1\le i,j\le n$

If $\rho\leq\sigma$, is $\operatorname{rank}(\rho)\leq\operatorname{rank}(\sigma)$?

Prove that V is an identity operator

Relaxed Loewner-order inequalities for matrix modulus

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