Question

Calculation of the $3\times 3$ exponent matrix via Cayley-Hamilton theorem.

score 107 · Answer 1 · 2023-03-10 19:59:23

107

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Calculation of the $3\times 3$ exponent matrix via Cayley-Hamilton theorem.

Published on 10 Mar 2023 - 19:59

score 77 · Answer 2 · 2023-03-28 21:04:37

77

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Showing there exists an $n\times n$ matrix that solves a given polynomial iff $n$ is even

Published on 28 Mar 2023 - 21:04

score 126 · Answer 3 · 2023-04-05 00:19:35

126

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Cayley-Hamilton proof using linear discrete-time systems

Published on 05 Apr 2023 - 0:19

score 88 · Answer 4 · 2023-04-27 11:19:52

88

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$A$ is a square matrix of order $2$ with real entries and ${\rm Tr}(A)+|A|=2$. Show that $|A^2+|A|\cdot A+{\rm Tr}(A)I_2|\geq 4$

Published on 27 Apr 2023 - 11:19

score 766 · Answer 5 · 2023-05-06 03:14:01

766

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Let $A$ and $B$ be two square matrices of order $2\times 2$, where $\det(A)=1$ and $\det(B)=2$ then value of $\det(A+\alpha B)-\det(\alpha A+B)$

Published on 06 May 2023 - 3:14

score 58 · Answer 6 · 2023-05-30 04:55:43

58

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An $n\times n$ matrix, $n\ge 2$ with characteristic polynomial $x^{n-2}(x^2-1)$

Published on 30 May 2023 - 4:55

score 108 · Answer 7 · 2023-06-28 12:50:23

108

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Proof of Cayley-Hamilton theorem over any field $\Bbb K$

Published on 28 Jun 2023 - 12:50

score 47 · Answer 8 · 2023-07-03 06:37:31

47

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Let $A \in M_n(\mathbb R)$ such that $A^2+A+5I_n = 0$. Find the characteristic polynomial of $A$

Published on 03 Jul 2023 - 6:37

score 150 · Answer 9 · 2023-09-28 08:53:17

150

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How does the Cayley–Hamilton theorem give me a formula for eigenvectors

Published on 28 Sep 2023 - 8:53

score 80 · Answer 10 · 2024-01-30 15:39:29

80

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Given a $3\times 3$ $\operatorname{adj} A$, find $A$

Published on 30 Jan 2024 - 15:39

score 38 · Answer 11 · 2024-03-09 07:42:33

38

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How to understand a situation where one can use Nakayama's lemma even when the situation is not Tailor-made.

Published on 09 Mar 2024 - 7:42

score 117 · Answer 12 · 2024-03-21 08:11:12

117

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Is this Corollary a historical or modern product?

Published on 21 Mar 2024 - 8:11

score 613 · Answer 13 · 2026-03-25 03:19:46

613

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Proving the continuation of the Cayley-Hamilton theorem from Schur's triangularization theorem

Published on 25 Mar 2026 - 3:19

score 1.3k · Answer 14 · 2015-06-22 05:58:58

1.3k

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Inverse of $A$ as a linear combination of $A$

Published on 22 Jun 2015 - 5:58

score 6.8k · Answer 15 · 2016-04-23 14:38:13

6.8k

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How many ways are there to prove Cayley-Hamilton Theorem?

Published on 23 Apr 2016 - 14:38

List Question

Calculation of the $3\times 3$ exponent matrix via Cayley-Hamilton theorem.

Showing there exists an $n\times n$ matrix that solves a given polynomial iff $n$ is even

Cayley-Hamilton proof using linear discrete-time systems

$A$ is a square matrix of order $2$ with real entries and ${\rm Tr}(A)+|A|=2$. Show that $|A^2+|A|\cdot A+{\rm Tr}(A)I_2|\geq 4$

Let $A$ and $B$ be two square matrices of order $2\times 2$, where $\det(A)=1$ and $\det(B)=2$ then value of $\det(A+\alpha B)-\det(\alpha A+B)$

An $n\times n$ matrix, $n\ge 2$ with characteristic polynomial $x^{n-2}(x^2-1)$

Proof of Cayley-Hamilton theorem over any field $\Bbb K$

Let $A \in M_n(\mathbb R)$ such that $A^2+A+5I_n = 0$. Find the characteristic polynomial of $A$

How does the Cayley–Hamilton theorem give me a formula for eigenvectors

Given a $3\times 3$ $\operatorname{adj} A$, find $A$

How to understand a situation where one can use Nakayama's lemma even when the situation is not Tailor-made.

Is this Corollary a historical or modern product?

Proving the continuation of the Cayley-Hamilton theorem from Schur's triangularization theorem

Inverse of $A$ as a linear combination of $A$

How many ways are there to prove Cayley-Hamilton Theorem?

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