List questions from matrix-congruences

Published on 10 Jun 2021 - 23:34

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How to conclude that matrices $A$ and $B$ are congruent?

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Show the relation between singular values of $A$ and $B^*AB$

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Is Same signs of determinants of $A$ and $B$ $\implies P^tAP =B$

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Matrix congruences

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Calculate maximum number of independent columns of a modular matrix

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How to convert this symmetric matrix to normal form?

Published on 19 Nov 2021 - 9:01

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Congruence of Matrices in Knot theory

Published on 16 Dec 2021 - 19:47

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$A,B \in M_3(\mathbb{R}) $ such that $A,B$ are symmetric. Find all values of $k\in \mathbb{N}$ such that $A^k , B^k$ are congruent.

Published on 05 Feb 2022 - 11:35

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Could we tell whether two matrices are congruent only by its eigenvalues? if not, How many conditions do we need?

Published on 24 Oct 2022 - 4:17

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Congruence between Symmetric and non-Symmetric Matrices for Quadratic Form

Published on 14 Dec 2022 - 7:46

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telling if two matrices are congruent and computing the N matric s.t A=N$^T$BN

Published on 19 Dec 2022 - 21:31

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Canonical form of a hermitian matrix with respect to congruence

Published on 08 Jan 2023 - 15:49

List Question

Showing that a certain binary matrix cannot be congruent to the null matrix

How to conclude that matrices $A$ and $B$ are congruent?

Show the relation between singular values of $A$ and $B^*AB$

Is Same signs of determinants of $A$ and $B$ $\implies P^tAP =B$

Matrix congruences

Calculate maximum number of independent columns of a modular matrix

How to convert this symmetric matrix to normal form?

Congruence of Matrices in Knot theory

$A,B \in M_3(\mathbb{R}) $ such that $A,B$ are symmetric. Find all values of $k\in \mathbb{N}$ such that $A^k , B^k$ are congruent.

Could we tell whether two matrices are congruent only by its eigenvalues? if not, How many conditions do we need?

Congruence between Symmetric and non-Symmetric Matrices for Quadratic Form

telling if two matrices are congruent and computing the N matric s.t A=N$^T$BN

Canonical form of a hermitian matrix with respect to congruence

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