List questions from positive-definite

Published on 25 Mar 2026 - 3:21

25

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If $A$ is positive definite and $Ax\le b$ can I say that $x\le A^{-1}b$?

Published on 17 Oct 2018 - 18:42

456

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Trace inequality for a product of p.s.d. matrices and their pseudo inverse.

Published on 19 Mar 2026 - 8:45

62

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integral involves positive definite function and Bessel function

Published on 30 Oct 2018 - 19:35

1k

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LU decomposition of SPD matrix without partial pivoting?

Published on 25 Mar 2026 - 9:34

3.6k

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Positive Definite Matrix Norm

Published on 04 Nov 2018 - 21:38

291

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Ways to check positive definiteness of bilinear form

Published on 25 Mar 2026 - 4:41

907

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The true meaning of eigenvalues and eigenvectors, and positive (semi) definite matrix?

Published on 25 Mar 2026 - 7:48

385

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Show that the matrix is positive definite

Published on 25 Mar 2026 - 0:09

498

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Prove the following set of unit vectors is orthogonal.

Published on 25 Mar 2026 - 9:28

22

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For a positive semi-definite $d\times d$ matrix $A$, $ (\text{det}(AS))^{\frac{1}{d}}\leq\frac{1}{d}\text{Tr}(AS) $ for every $S\in\text{SPD}_{d}$.

Published on 12 Nov 2018 - 9:06

244

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bilinear form only positive or negative

Published on 25 Mar 2026 - 4:35

51

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Conditions for a certain parametric matrix to be positive definite

Published on 13 Nov 2018 - 16:52

141

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Let $A$ be a positive definite matrix and $B$ be a positive semi-definite matrix. Then $AB$ is diagonalizable.

Published on 25 Mar 2026 - 7:45

270

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What is the maximum value of $x^TAx$ subject to $x\in\{\pm1\}^n$?

Published on 14 Mar 2026 - 9:40

List Question

Hessian of negative log-likelihood of logistic regression is positive definite?

If $A$ is positive definite and $Ax\le b$ can I say that $x\le A^{-1}b$?

Trace inequality for a product of p.s.d. matrices and their pseudo inverse.

integral involves positive definite function and Bessel function

LU decomposition of SPD matrix without partial pivoting?

Positive Definite Matrix Norm

Ways to check positive definiteness of bilinear form

The true meaning of eigenvalues and eigenvectors, and positive (semi) definite matrix?

Show that the matrix is positive definite

Prove the following set of unit vectors is orthogonal.

For a positive semi-definite $d\times d$ matrix $A$, $ (\text{det}(AS))^{\frac{1}{d}}\leq\frac{1}{d}\text{Tr}(AS) $ for every $S\in\text{SPD}_{d}$.

bilinear form only positive or negative

Conditions for a certain parametric matrix to be positive definite

Let $A$ be a positive definite matrix and $B$ be a positive semi-definite matrix. Then $AB$ is diagonalizable.

What is the maximum value of $x^TAx$ subject to $x\in\{\pm1\}^n$?

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