Question

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

score 257 · Answer 1 · 2026-04-15 18:35:08

257

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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 15 Apr 2026 - 18:35

score 202 · Answer 2 · 2026-04-13 04:30:53

202

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Hamilton-Cayley Theorem for Vector Spaces Over Any Field

Published on 13 Apr 2026 - 4:30

score 503 · Answer 3 · 2026-05-11 04:14:04

503

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Why Nilpotent Matrix is not Null matrix always?

Published on 11 May 2026 - 4:14

score 200 · Answer 4 · 2026-04-10 21:58:27

200

Views

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

Published on 10 Apr 2026 - 21:58

score 834 · Answer 5 · 2026-04-12 09:09:38

834

Views

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

Published on 12 Apr 2026 - 9:09

score 162 · Answer 6 · 2026-04-09 04:21:13

162

Views

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

Published on 09 Apr 2026 - 4:21

score 127 · Answer 7 · 2026-04-17 14:37:51

127

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 17 Apr 2026 - 14:37

score 259 · Answer 8 · 2026-04-11 23:08:46

259

Views

Proving Cayley Hamilton theorem in a different way

Published on 11 Apr 2026 - 23:08

score 90 · Answer 9 · 2026-04-17 13:36:37

90

Views

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

Published on 17 Apr 2026 - 13:36

score 96 · Answer 10 · 2026-05-10 17:35:48

96

Views

Cayley-Hamilton in Macaulay2

Published on 10 May 2026 - 17:35

score 66 · Answer 11 · 2026-04-15 07:24:11

66

Views

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

Published on 15 Apr 2026 - 7:24

score 114 · Answer 12 · 2026-04-16 16:21:27

114

Views

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

Published on 16 Apr 2026 - 16:21

score 321 · Answer 13 · 2026-04-14 11:57:40

321

Views

Prove Cayley-Hamilton theorem

Published on 14 Apr 2026 - 11:57

score 313 · Answer 14 · 2026-04-14 15:19:01

313

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Proofs of the Cayley-Hamilton Theorem

Published on 14 Apr 2026 - 15:19

score 528 · Answer 15 · 2026-04-12 03:10:03

528

Views

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

Published on 12 Apr 2026 - 3:10

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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