Question

Establish if True or False: Any polynomial of degree $n$ with leading coefficient $(-1)^n$ is the characteristic polynomial

score 254 · Answer 1 · 2021-05-04 16:38:16

254

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Establish if True or False: Any polynomial of degree $n$ with leading coefficient $(-1)^n$ is the characteristic polynomial

Published on 04 May 2021 - 16:38

score 199 · Answer 2 · 2021-05-07 20:26:19

199

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Hamilton-Cayley Theorem for Vector Spaces Over Any Field

Published on 07 May 2021 - 20:26

score 499 · Answer 3 · 2021-05-20 12:35:30

499

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Why Nilpotent Matrix is not Null matrix always?

Published on 20 May 2021 - 12:35

score 197 · Answer 4 · 2021-06-12 03:17:00

197

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Can we determine higher powers of a matrix in terms of lower powered matrices?

Published on 12 Jun 2021 - 3:17

score 831 · Answer 5 · 2021-07-14 04:00:49

831

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Find trace and determinant of matrix $A$ such that $A^2 = I$.

Published on 14 Jul 2021 - 4:00

score 159 · Answer 6 · 2021-08-08 19:16:04

159

Views

Is the Putzer algorithm markedly more efficient than the Cayley-Hamilton reduction of $\exp(At)$?

Published on 08 Aug 2021 - 19:16

score 124 · Answer 7 · 2021-08-11 03:55:05

124

Views

Prove that $P^k=P$ for any $k \in \mathbb{N}$ where $1$ is the only eigenvalue of $P$ implies $P=I$.

Published on 11 Aug 2021 - 3:55

score 256 · Answer 8 · 2021-09-06 06:12:59

256

Views

Proving Cayley Hamilton theorem in a different way

Published on 06 Sep 2021 - 6:12

score 85 · Answer 9 · 2021-09-13 11:59:38

85

Views

Characteristic polynomial of a perturbed matrix (on the first column) as function of the original characteristic polynomial

Published on 13 Sep 2021 - 11:59

score 95 · Answer 10 · 2026-03-25 06:08:39

95

Views

Cayley-Hamilton in Macaulay2

Published on 25 Mar 2026 - 6:08

score 64 · Answer 11 · 2021-09-28 21:04:31

64

Views

Why can we substitute matrix and eigenvalues into other than the characteristic polynomial (Cayley Hamilton)

Published on 28 Sep 2021 - 21:04

score 111 · Answer 12 · 2021-10-19 14:18:44

111

Views

Find $5\times5$ invertible matrix $A$ over $\mathbb{F}_3$ such that $A^{-1} = 2A^3 +2I$, $A \neq I$

Published on 19 Oct 2021 - 14:18

score 318 · Answer 13 · 2021-12-01 10:37:31

318

Views

Prove Cayley-Hamilton theorem

Published on 01 Dec 2021 - 10:37

score 310 · Answer 14 · 2021-12-08 21:23:04

310

Views

Proofs of the Cayley-Hamilton Theorem

Published on 08 Dec 2021 - 21:23

score 525 · Answer 15 · 2021-12-28 13:55:02

525

Views

About a proof of Cayley-Hamilton theorem in "Linear Algebra" by Ichiro Satake.

Published on 28 Dec 2021 - 13:55

List Question

Establish if True or False: Any polynomial of degree $n$ with leading coefficient $(-1)^n$ is the characteristic polynomial

Hamilton-Cayley Theorem for Vector Spaces Over Any Field

Why Nilpotent Matrix is not Null matrix always?

Can we determine higher powers of a matrix in terms of lower powered matrices?

Find trace and determinant of matrix $A$ such that $A^2 = I$.

Is the Putzer algorithm markedly more efficient than the Cayley-Hamilton reduction of $\exp(At)$?

Prove that $P^k=P$ for any $k \in \mathbb{N}$ where $1$ is the only eigenvalue of $P$ implies $P=I$.

Proving Cayley Hamilton theorem in a different way

Characteristic polynomial of a perturbed matrix (on the first column) as function of the original characteristic polynomial

Cayley-Hamilton in Macaulay2

Why can we substitute matrix and eigenvalues into other than the characteristic polynomial (Cayley Hamilton)

Find $5\times5$ invertible matrix $A$ over $\mathbb{F}_3$ such that $A^{-1} = 2A^3 +2I$, $A \neq I$

Prove Cayley-Hamilton theorem

Proofs of the Cayley-Hamilton Theorem

About a proof of Cayley-Hamilton theorem in "Linear Algebra" by Ichiro Satake.

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