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On the positve definiteness of a particular matrix and inverse

score 52 · Answer 1 · 2026-03-25 03:03:07

52

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On the positve definiteness of a particular matrix and inverse

Published on 25 Mar 2026 - 3:03

score 36 · Answer 2 · 2026-04-16 15:51:03

36

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A neat way of representing a matrix, where each column is a different matrix-vector product?

Published on 16 Apr 2026 - 15:51

score 2k · Answer 3 · 2026-04-09 04:18:10

2k

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Arbitrary operator as a sum of Hermitian operators

Published on 09 Apr 2026 - 4:18

score 1.5k · Answer 4 · 2026-04-15 08:03:12

1.5k

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Let $T: \mathbb{R}^4 \to \mathbb{R}^4$ be any linear transformation. Then how can I show that $T$ has a proper non zero invariant subspace.

Published on 15 Apr 2026 - 8:03

score 3.7k · Answer 5 · 2026-04-09 07:21:18

3.7k

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How to construct a matrix given the null basis of A?

Published on 09 Apr 2026 - 7:21

score 1k · Answer 6 · 2026-04-14 01:07:56

1k

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Hunting for a basis: Rational Canonical Form

Published on 14 Apr 2026 - 1:07

score 249 · Answer 7 · 2026-04-09 14:30:00

249

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Finding change of variables to give linear homogeneous system

Published on 09 Apr 2026 - 14:30

score 181 · Answer 8 · 2026-04-16 06:49:04

181

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How to prove $\rm{tr}(A)=\rm{tr}(B)$ for real $2018\times2018$-matrices such that $A^{2018}=I=B^{2018}$ and $AB=BA$ and $\rm{tr}(AB)=2018$

Published on 16 Apr 2026 - 6:49

score 235 · Answer 9 · 2026-04-29 12:52:11

235

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Equivalence classes in $M_n(\mathbb{R})$

Published on 29 Apr 2026 - 12:52

score 93 · Answer 10 · 2026-04-13 07:04:10

93

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How to find eigenvalues of the following matrix

Published on 13 Apr 2026 - 7:04

score 38 · Answer 11 · 2026-04-30 08:20:44

38

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Smith form for a matrix

Published on 30 Apr 2026 - 8:20

score 318 · Answer 12 · 2026-04-16 15:50:12

318

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If $C$ is nonsingular, show that $A$ and $C^TAC$ have the same rank.

Published on 16 Apr 2026 - 15:50

score 252 · Answer 13 · 2026-04-14 17:36:09

Let $A$ be a square matrix. Prove that $A$ is non-singular if and only if $AX=b$ has a solution for each $b$.

score 76 · Answer 14 · 2026-04-15 15:02:28

76

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prove: $||A-B||_{F}\geq||A-T(A)||_{F}$ as: given $A, B \in M_{n\times n}(\mathbb{R})$ , and $B$ is symmetric

Published on 15 Apr 2026 - 15:02

score 327 · Answer 15 · 2026-04-16 23:11:36

327

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Characterization of Matrices with only one Element in every Row and Column

Published on 16 Apr 2026 - 23:11

List Question

On the positve definiteness of a particular matrix and inverse

A neat way of representing a matrix, where each column is a different matrix-vector product?

Arbitrary operator as a sum of Hermitian operators

Let $T: \mathbb{R}^4 \to \mathbb{R}^4$ be any linear transformation. Then how can I show that $T$ has a proper non zero invariant subspace.

How to construct a matrix given the null basis of A?

Hunting for a basis: Rational Canonical Form

Finding change of variables to give linear homogeneous system

How to prove $\rm{tr}(A)=\rm{tr}(B)$ for real $2018\times2018$-matrices such that $A^{2018}=I=B^{2018}$ and $AB=BA$ and $\rm{tr}(AB)=2018$

Equivalence classes in $M_n(\mathbb{R})$

How to find eigenvalues of the following matrix

Smith form for a matrix

If $C$ is nonsingular, show that $A$ and $C^TAC$ have the same rank.

Let $A$ be a square matrix. Prove that $A$ is non-singular if and only if $AX=b$ has a solution for each $b$.

prove: $||A-B||_{F}\geq||A-T(A)||_{F}$ as: given $A, B \in M_{n\times n}(\mathbb{R})$ , and $B$ is symmetric

Characterization of Matrices with only one Element in every Row and Column

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