List questions from positive-definite

Published on 10 Jul 2018 - 19:28

125

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Prove a rank equality for PSD matrices

Published on 12 Jul 2018 - 18:09

120

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Equivalence in positive definiteness of $AB$ and $BA$

Published on 13 Jul 2018 - 17:28

208

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Eigenvalues of element-wise ordered matrices

Published on 16 Jul 2018 - 18:55

168

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For a real square matrix $S$ with all eigenvalues on the imaginary axis, does the following hold?

Published on 16 Jul 2018 - 19:04

154

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An upper bound for $trace(XYXZ)$ in terms of $trace(X^2YZ)$

Published on 16 Jul 2018 - 23:50

496

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operator concavity of a function involving trace and logarithm

Published on 17 Jul 2018 - 21:49

216

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$\operatorname{trace}(B)>0$, and $C$ is a Hermitian positive definite, is $\operatorname{trace}(BC)\geq 0$?

Published on 19 Jul 2018 - 15:01

166

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Matrix equation with symmetric and positive definite matrices

Published on 25 Jul 2018 - 20:33

702

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Existence of a similar positive definite matrix

Published on 26 Jul 2018 - 14:13

98

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Volume of $M:=\big\{(x,y,z)\in \mathbb{R}^3\,:\,ax^2+2bxy+cy^2\leq z \leq 3\big\}$

Published on 25 Mar 2026 - 1:18

1.3k

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If $A$ is positive definite prove that $(x^TAx)(x^TA^{-1}x) \geq 1$

Published on 08 Aug 2018 - 7:37

52

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On the positve definiteness of a particular matrix and inverse

Published on 25 Mar 2026 - 3:03

443

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Writing a convex quadratic constraint in SOC form

Published on 10 Aug 2018 - 17:37

363

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Positive definiteness of a multivariate polynomial function

Published on 25 Mar 2026 - 2:59

List Question

Positive definite in the limit

Prove a rank equality for PSD matrices

Equivalence in positive definiteness of $AB$ and $BA$

Eigenvalues of element-wise ordered matrices

For a real square matrix $S$ with all eigenvalues on the imaginary axis, does the following hold?

An upper bound for $trace(XYXZ)$ in terms of $trace(X^2YZ)$

operator concavity of a function involving trace and logarithm

$\operatorname{trace}(B)>0$, and $C$ is a Hermitian positive definite, is $\operatorname{trace}(BC)\geq 0$?

Matrix equation with symmetric and positive definite matrices

Existence of a similar positive definite matrix

Volume of $M:=\big\{(x,y,z)\in \mathbb{R}^3\,:\,ax^2+2bxy+cy^2\leq z \leq 3\big\}$

If $A$ is positive definite prove that $(x^TAx)(x^TA^{-1}x) \geq 1$

On the positve definiteness of a particular matrix and inverse

Writing a convex quadratic constraint in SOC form

Positive definiteness of a multivariate polynomial function

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