Question

Can an $n \times n$ matrix satisfy an $n$ degree polynomial equation other than its characteristic polynomial equation?

score 1.2k · Answer 1 · 2026-03-25 20:35:56

1.2k

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Can an $n \times n$ matrix satisfy an $n$ degree polynomial equation other than its characteristic polynomial equation?

Published on 25 Mar 2026 - 20:35

score 540 · Answer 2 · 2026-03-25 11:10:53

540

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Prove that every permutation matrix satisfies its characteristic polynomial.

Published on 25 Mar 2026 - 11:10

score 445 · Answer 3 · 2026-03-25 19:04:49

445

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What Is the meaning of at the algebraic multiplicity?

Published on 25 Mar 2026 - 19:04

score 789 · Answer 4 · 2026-03-26 01:01:43

789

Views

Characteristic & minimal polynomial & geometric multiplicity

Published on 26 Mar 2026 - 1:01

score 174 · Answer 5 · 2026-05-10 20:21:34

174

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Can we apply here the Cayley–Hamilton theorem?

Published on 10 May 2026 - 20:21

score 125 · Answer 6 · 2026-03-25 22:05:36

125

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If $A$ and $B$ are matrices in $\textsf{M}_{n \times n}(\mathbb{R})$, prove or refute that $AB$ and $BA$ have the same minimal polynomial

Published on 25 Mar 2026 - 22:05

score 143 · Answer 7 · 2026-03-25 19:06:39

143

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The minimal and characteristic polynomial of the linear operator $T_P(M)=PMP^{-1}$ acting on $S(3)$

Published on 25 Mar 2026 - 19:06

score 525 · Answer 8 · 2026-03-25 19:07:05

525

Views

{$v,f(v),f^2(v),\ldots,f^{n-1}(v)$} is a basis of $V$ if the minimal polynomial of $f$ is equal to the characteristic polynomial of $f$

Published on 25 Mar 2026 - 19:07

score 119 · Answer 9 · 2026-03-25 20:35:09

119

Views

Computing characteristic polynomial of $4 \times 4$ matrix

Published on 25 Mar 2026 - 20:35

score 62 · Answer 10 · 2026-03-25 19:00:22

62

Views

Factor: $\det\left[\begin{smallmatrix}\lambda-(1-a) & -a \\ -b & \lambda - (1-b)\end{smallmatrix}\right]=0$

Published on 25 Mar 2026 - 19:00

score 269 · Answer 11 · 2026-03-25 12:54:14

269

Views

Alternative way to find the eigenvalues of a matrix.

Published on 25 Mar 2026 - 12:54

score 901 · Answer 12 · 2026-05-10 14:59:08

901

Views

Showing a matrix is non-derogatory

Published on 10 May 2026 - 14:59

score 209 · Answer 13 · 2026-05-10 16:07:28

209

Views

Polynomials $\&$ Matrices

Published on 10 May 2026 - 16:07

score 304 · Answer 14 · 2026-03-25 19:05:34

304

Views

How to determine $A^n$ based on the division of its characteristic polynomial?

Published on 25 Mar 2026 - 19:05

score 5.1k · Answer 15 · 2026-03-25 19:10:31

5.1k

Views

Is there a fast way to get the characteristic polynomial of this symmetric matrix?

Published on 25 Mar 2026 - 19:10

List Question

Can an $n \times n$ matrix satisfy an $n$ degree polynomial equation other than its characteristic polynomial equation?

Prove that every permutation matrix satisfies its characteristic polynomial.

What Is the meaning of at the algebraic multiplicity?

Characteristic & minimal polynomial & geometric multiplicity

Can we apply here the Cayley–Hamilton theorem?

If $A$ and $B$ are matrices in $\textsf{M}_{n \times n}(\mathbb{R})$, prove or refute that $AB$ and $BA$ have the same minimal polynomial

The minimal and characteristic polynomial of the linear operator $T_P(M)=PMP^{-1}$ acting on $S(3)$

{$v,f(v),f^2(v),\ldots,f^{n-1}(v)$} is a basis of $V$ if the minimal polynomial of $f$ is equal to the characteristic polynomial of $f$

Computing characteristic polynomial of $4 \times 4$ matrix

Factor: $\det\left[\begin{smallmatrix}\lambda-(1-a) & -a \\ -b & \lambda - (1-b)\end{smallmatrix}\right]=0$

Alternative way to find the eigenvalues of a matrix.

Showing a matrix is non-derogatory

Polynomials $\&$ Matrices

How to determine $A^n$ based on the division of its characteristic polynomial?

Is there a fast way to get the characteristic polynomial of this symmetric matrix?

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