Question

Looking for proof of " two congruent symmetric matrices with real entries have the same numbers of positive, negative, and zero eigenvalues "

score 636 · Answer 1 · 2026-04-13 13:44:20

636

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Looking for proof of " two congruent symmetric matrices with real entries have the same numbers of positive, negative, and zero eigenvalues "

Published on 13 Apr 2026 - 13:44

score 280 · Answer 2 · 2026-04-14 13:30:48

280

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Example of matrices with some interesting properties like same characteristic and minimal polynomial etc.

Published on 14 Apr 2026 - 13:30

score 145 · Answer 3 · 2026-04-12 04:36:25

145

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Prove $A$ is scalar matrix

Published on 12 Apr 2026 - 4:36

score 311 · Answer 4 · 2026-04-10 19:47:22

311

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What is the minimal polynomial of $A^2$?

Published on 10 Apr 2026 - 19:47

score 133 · Answer 5 · 2026-04-12 12:32:04

133

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Prove that $\mathrm{span}\{ I,A,A^2... \} = \mathrm{span} \{ I,A,A^2,..., A^{k-1}\}$

Published on 12 Apr 2026 - 12:32

score 2k · Answer 6 · 2026-04-13 13:58:19

2k

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How to find eigenvalues of this 3x3 Jacobian Matrix

Published on 13 Apr 2026 - 13:58

score 2.4k · Answer 7 · 2026-04-11 04:15:50

2.4k

Views

Proving if A is an Hermitian matrix with nonnegative eigenvalues, A is positive semidefinite.

Published on 11 Apr 2026 - 4:15

score 2.7k · Answer 8 · 2026-04-11 23:09:24

2.7k

Views

Proving if $A$ is an $n\times n$ positive semi-definite matrix, A is Hermitian with non-negative eigenvalues.

Published on 11 Apr 2026 - 23:09

score 359 · Answer 9 · 2026-04-13 04:17:31

359

Views

Finding solutions of system of differential equations with eigenvectors

Published on 13 Apr 2026 - 4:17

score 1.6k · Answer 10 · 2026-04-12 07:26:29

1.6k

Views

Stochastic matrix - semisimple eigenvalue

Published on 12 Apr 2026 - 7:26

score 1.4k · Answer 11 · 2026-04-10 08:38:20

1.4k

Views

given two eigevectors with two eigenvalues and no A, compute Av?

Published on 10 Apr 2026 - 8:38

score 138 · Answer 12 · 2026-04-13 17:02:32

138

Views

Prove $\Xi (I - P)$ has eigenvalues in the non-negative real half-plane.

Published on 13 Apr 2026 - 17:02

score 103 · Answer 13 · 2026-04-14 01:20:36

103

Views

Factorize matrix determinant

Published on 14 Apr 2026 - 1:20

score 1.7k · Answer 14 · 2026-04-13 01:37:49

1.7k

Views

MATLAB Eigenvalues

Published on 13 Apr 2026 - 1:37

score 27 · Answer 15 · 2026-04-13 04:25:39

27

Views

Complex numbers property proof.

Published on 13 Apr 2026 - 4:25

List Question

Looking for proof of " two congruent symmetric matrices with real entries have the same numbers of positive, negative, and zero eigenvalues "

Example of matrices with some interesting properties like same characteristic and minimal polynomial etc.

Prove $A$ is scalar matrix

What is the minimal polynomial of $A^2$?

Prove that $\mathrm{span}\{ I,A,A^2... \} = \mathrm{span} \{ I,A,A^2,..., A^{k-1}\}$

How to find eigenvalues of this 3x3 Jacobian Matrix

Proving if A is an Hermitian matrix with nonnegative eigenvalues, A is positive semidefinite.

Proving if $A$ is an $n\times n$ positive semi-definite matrix, A is Hermitian with non-negative eigenvalues.

Finding solutions of system of differential equations with eigenvectors

Stochastic matrix - semisimple eigenvalue

given two eigevectors with two eigenvalues and no A, compute Av?

Prove $\Xi (I - P)$ has eigenvalues in the non-negative real half-plane.

Factorize matrix determinant

MATLAB Eigenvalues

Complex numbers property proof.

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