Question

Let $A$ be a $(n \times n)$ complex matrix, and for $C$ a $(1 \times n)$ row vector let $W = \{\sum_{j=0}^{n-1}a_jCA^j:j=0,\dots,n-1\}\;.$

score 65 · Answer 1 · 2026-03-23 07:16:09

65

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Let $A$ be a $(n \times n)$ complex matrix, and for $C$ a $(1 \times n)$ row vector let $W = \{\sum_{j=0}^{n-1}a_jCA^j:j=0,\dots,n-1\}\;.$

Published on 23 Mar 2026 - 7:16

score 72 · Answer 2 · 2026-03-23 15:35:34

72

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Clarification on Cayley-Hamilton theorem

Published on 23 Mar 2026 - 15:35

score 1k · Answer 3 · 2026-03-23 14:29:54

1k

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Cayley-Hamilton theorem to compute this.

Published on 23 Mar 2026 - 14:29

score 202 · Answer 4 · 2026-03-23 10:22:31

202

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Mistake in Peter Lax Linear Algebra Caley Hamilton proof

Published on 23 Mar 2026 - 10:22

score 51 · Answer 5 · 2026-03-22 17:15:22

51

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Show that $v$ is a eigenvector of $q(A)$ with respect to $p(\lambda)$.

Published on 22 Mar 2026 - 17:15

score 491 · Answer 6 · 2026-03-23 14:03:30

491

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How to prove a matrix is invertible given a polynomial that annihilates it?

Published on 23 Mar 2026 - 14:03

score 114 · Answer 7 · 2026-03-23 14:39:15

114

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Finding The Characteristic Polynomial of a Matrix With Integer Sum Coefficients.

Published on 23 Mar 2026 - 14:39

score 86 · Answer 8 · 2026-03-23 09:31:50

86

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$ X^{25} = A $ in $ M_{2}(\mathbb{R}) $

Published on 23 Mar 2026 - 9:31

score 110 · Answer 9 · 2026-03-23 11:22:45

110

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For $2 \times 2$ matrices $AB=-BA$ with $BA$ not $0$, prove that $\mathrm{tr}(A)=\mathrm{tr}(B)=\mathrm{tr}(AB)=0$

Published on 23 Mar 2026 - 11:22

score 761 · Answer 10 · 2026-03-22 21:13:58

761

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$A^2=-I_4$. Find possible values of minimal polynomial and characteristic polynomial

Published on 22 Mar 2026 - 21:13

score 115 · Answer 11 · 2026-03-22 18:31:04

115

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Write $m_{I-A}$ (the minimal polynomial of $I-A$) in terms of $m_A$ and conclude: $\deg(m_A)=\deg(m_{I-A})$

Published on 22 Mar 2026 - 18:31

score 206 · Answer 12 · 2026-03-25 04:38:03

206

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Prove that characteristic polynomial = minimal polynomial

Published on 25 Mar 2026 - 4:38

score 50 · Answer 13 · 2026-03-25 06:00:34

50

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Dimension on span of End(V) composition

Published on 25 Mar 2026 - 6:00

score 92 · Answer 14 · 2026-03-22 18:29:25

92

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Which one of the following are correct?

Published on 22 Mar 2026 - 18:29

score 447 · Answer 15 · 2026-03-25 04:42:52

447

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Can I use the Cayley-Hamilton theorem to determine $ \det(A) $ from the identity $ {A}^{-1} = {A}^{2} - c {I}_{n} $?

Published on 25 Mar 2026 - 4:42

List Question

Let $A$ be a $(n \times n)$ complex matrix, and for $C$ a $(1 \times n)$ row vector let $W = \{\sum_{j=0}^{n-1}a_jCA^j:j=0,\dots,n-1\}\;.$

Clarification on Cayley-Hamilton theorem

Cayley-Hamilton theorem to compute this.

Mistake in Peter Lax Linear Algebra Caley Hamilton proof

Show that $v$ is a eigenvector of $q(A)$ with respect to $p(\lambda)$.

How to prove a matrix is invertible given a polynomial that annihilates it?

Finding The Characteristic Polynomial of a Matrix With Integer Sum Coefficients.

$ X^{25} = A $ in $ M_{2}(\mathbb{R}) $

For $2 \times 2$ matrices $AB=-BA$ with $BA$ not $0$, prove that $\mathrm{tr}(A)=\mathrm{tr}(B)=\mathrm{tr}(AB)=0$

$A^2=-I_4$. Find possible values of minimal polynomial and characteristic polynomial

Write $m_{I-A}$ (the minimal polynomial of $I-A$) in terms of $m_A$ and conclude: $\deg(m_A)=\deg(m_{I-A})$

Prove that characteristic polynomial = minimal polynomial

Dimension on span of End(V) composition

Which one of the following are correct?

Can I use the Cayley-Hamilton theorem to determine $ \det(A) $ from the identity $ {A}^{-1} = {A}^{2} - c {I}_{n} $?

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