List questions from linear-algebra

Published on 14 May 2026 - 7:11

2k

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If $AB = -BA$, then tr$(A) = $ tr$(B) = 0 $

Published on 11 May 2026 - 8:24

48

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Perturbation of a set of vectors which spans the whole space

Published on 14 May 2026 - 18:25

160

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How to show a rational polynomial is irreducible in $\mathbb{Q}[a,b,c]$?

Published on 14 Apr 2026 - 18:38

146

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Exponential series problem

Published on 10 Apr 2026 - 14:17

33

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General version of Cramer's rule

Published on 11 Apr 2026 - 19:37

45

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Indices algebra problem

Published on 17 Apr 2026 - 6:03

225

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How to arrive at $ \frac{\partial }{\partial X} \log(\mathrm{det}(I + A X B^\top )) = A^\top (I +B X^\top A^\top )^{-1} B$?

Published on 14 Apr 2026 - 8:30

28

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$a_{1}v_{1}+a_{2}v_{2}+\cdots+a_{i}v_{i}$=$u$, but some of $a_{j}$ is not unique

Published on 15 Apr 2026 - 9:00

171

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Deduction of eigenvalues of the matrix $A$ which satisfies $x^t A A^t x = \alpha x^t x$?

Published on 16 Apr 2026 - 12:33

91

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For $\mathbb{S}$ subspace of $\mathbb{V}$, prove $L:\mathbb{V}\to\mathbb{V}$ such that Ker$(L)=\mathbb{S}$

Published on 15 Apr 2026 - 11:37

748

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Is there a necessary and sufficient condition for a square matrix to be able to diagonalize a symmetric square matrix?

Published on 15 Apr 2026 - 4:41

1.1k

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Eigenvalues of $A^tA$?

Published on 12 Apr 2026 - 5:17

187

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If $A$ and $B$ are matrices, what can we conclude if $AB = BA$

Published on 24 Apr 2026 - 9:43

293

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Solving equations using rectangular matrix

Published on 13 Apr 2026 - 9:19

List Question

Finding Rational Canonical Form

If $AB = -BA$, then tr$(A) = $ tr$(B) = 0 $

Perturbation of a set of vectors which spans the whole space

How to show a rational polynomial is irreducible in $\mathbb{Q}[a,b,c]$?

Exponential series problem

General version of Cramer's rule

Indices algebra problem

How to arrive at $ \frac{\partial }{\partial X} \log(\mathrm{det}(I + A X B^\top )) = A^\top (I +B X^\top A^\top )^{-1} B$?

$a_{1}v_{1}+a_{2}v_{2}+\cdots+a_{i}v_{i}$=$u$, but some of $a_{j}$ is not unique

Deduction of eigenvalues of the matrix $A$ which satisfies $x^t A A^t x = \alpha x^t x$?

For $\mathbb{S}$ subspace of $\mathbb{V}$, prove $L:\mathbb{V}\to\mathbb{V}$ such that Ker$(L)=\mathbb{S}$

Is there a necessary and sufficient condition for a square matrix to be able to diagonalize a symmetric square matrix?

Eigenvalues of $A^tA$?

If $A$ and $B$ are matrices, what can we conclude if $AB = BA$

Solving equations using rectangular matrix

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