Question

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

score 1.2k · Answer 1 · 2020-07-06 17:40:32

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 06 Jul 2020 - 17:40

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

540

Views

Prove that every permutation matrix satisfies its characteristic polynomial.

Published on 25 Mar 2026 - 11:10

score 444 · Answer 3 · 2020-07-10 15:35:11

444

Views

What Is the meaning of at the algebraic multiplicity?

Published on 10 Jul 2020 - 15:35

score 788 · Answer 4 · 2020-07-11 06:25:20

788

Views

Characteristic & minimal polynomial & geometric multiplicity

Published on 11 Jul 2020 - 6:25

score 173 · Answer 5 · 2026-03-25 11:10:40

173

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Can we apply here the Cayley–Hamilton theorem?

Published on 25 Mar 2026 - 11:10

score 124 · Answer 6 · 2020-07-14 16:58:56

124

Views

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 14 Jul 2020 - 16:58

score 142 · Answer 7 · 2020-07-17 23:00:06

142

Views

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

Published on 17 Jul 2020 - 23:00

score 524 · Answer 8 · 2020-07-20 02:46:52

524

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 20 Jul 2020 - 2:46

score 118 · Answer 9 · 2020-07-23 11:28:37

118

Views

Computing characteristic polynomial of $4 \times 4$ matrix

Published on 23 Jul 2020 - 11:28

score 61 · Answer 10 · 2020-07-30 20:54:07

61

Views

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

Published on 30 Jul 2020 - 20:54

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 898 · Answer 12 · 2016-11-13 21:08:05

898

Views

Showing a matrix is non-derogatory

Published on 13 Nov 2016 - 21:08

score 191 · Answer 13 · 2026-03-25 16:35:09

191

Views

Polynomials $\&$ Matrices

Published on 25 Mar 2026 - 16:35

score 303 · Answer 14 · 2026-03-22 05:23:12

303

Views

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

Published on 22 Mar 2026 - 5:23

score 5.1k · Answer 15 · 2026-03-22 04:28:12

5.1k

Views

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

Published on 22 Mar 2026 - 4:28

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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