List questions from positive-definite

Published on 25 Mar 2026 - 23:09

176

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How do I prove that $\sum_{i,j=1}^na_{ij}b_{ij} \geq 0$ if $A=(a_{ij})$ and $B=(b_{ij})$ are both positive semidefinite $n \times n$ matrices?

Published on 25 Mar 2026 - 12:51

64

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The relation between the trace of a positive definite matrix and the trace of the inverse of this matrix

Published on 25 Mar 2026 - 12:49

37

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Methods for Definiteness of a matrix are giving different results

Published on 25 Mar 2026 - 18:55

193

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spectral radius of products of symmetric positive definite matrices

Published on 26 Mar 2026 - 4:36

1.8k

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Proof that covariance matrix is positive semi-definite (and not positive definite)

Published on 25 Mar 2026 - 22:04

102

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find the trace of a $D^{-1}$ in $A=(B+C)D^{-1}$

Published on 25 Mar 2026 - 1:17

97

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A bound on the eigenvalues of a product

Published on 26 Mar 2026 - 4:30

1.3k

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Eigenvalues of a positive principal minors symmetric matrix

Published on 25 Sep 2019 - 15:53

89

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Positive definiteness of a submatrix

Published on 25 Sep 2019 - 18:08

223

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log of determinant of PD matrix

Published on 26 Sep 2019 - 8:59

155

Views

How can we prove that If $A \in \mathbb{R}^{m\times n}$ is a full rank matrix and $m\ge n$, then $A^\top A$ is a positive definite matrix?

Published on 27 Sep 2019 - 18:20

2.1k

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Minima of positive definite and positive semidefinite functions

Published on 25 Mar 2026 - 22:03

1.1k

Views

Positive definite when multiplying by two matrices

Published on 25 Mar 2026 - 20:34

13.9k

Views

Power method for finding all eigenvectors

Published on 25 Apr 2014 - 14:35

List Question

Why do we ensure that this function is positive?

How do I prove that $\sum_{i,j=1}^na_{ij}b_{ij} \geq 0$ if $A=(a_{ij})$ and $B=(b_{ij})$ are both positive semidefinite $n \times n$ matrices?

The relation between the trace of a positive definite matrix and the trace of the inverse of this matrix

Methods for Definiteness of a matrix are giving different results

spectral radius of products of symmetric positive definite matrices

Proof that covariance matrix is positive semi-definite (and not positive definite)

find the trace of a $D^{-1}$ in $A=(B+C)D^{-1}$

A bound on the eigenvalues of a product

Eigenvalues of a positive principal minors symmetric matrix

Positive definiteness of a submatrix

log of determinant of PD matrix

How can we prove that If $A \in \mathbb{R}^{m\times n}$ is a full rank matrix and $m\ge n$, then $A^\top A$ is a positive definite matrix?

Minima of positive definite and positive semidefinite functions

Positive definite when multiplying by two matrices

Power method for finding all eigenvectors

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