Question

$A^3 = A^2$ How can $A$'s minimal polynomial look like?

score 310 · Answer 1 · 2026-04-12 20:44:59

310

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$A^3 = A^2$ How can $A$'s minimal polynomial look like?

Published on 12 Apr 2026 - 20:44

score 175 · Answer 2 · 2026-04-12 10:07:04

175

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Minimal polynomial for module over $A$ such that $A[x]$ is not a PID

Published on 12 Apr 2026 - 10:07

score 248 · Answer 3 · 2026-05-05 07:37:54

248

Views

Find minimal polynomial of matrix with some given property

Published on 05 May 2026 - 7:37

score 40 · Answer 4 · 2026-04-11 03:24:57

40

Views

Clarification Regarding to prove diagonalisable operator iff Minimal Polynomial Splits and

Published on 11 Apr 2026 - 3:24

score 154 · Answer 5 · 2026-04-13 22:49:35

154

Views

Show that $F(T)$ is invertible if and only if it has no common factors with the minimal polynomial of T.

Published on 13 Apr 2026 - 22:49

score 259 · Answer 6 · 2026-04-14 17:14:17

259

Views

Find the minimal polynomial over $\mathbb{Q}(i)$

Published on 14 Apr 2026 - 17:14

score 661 · Answer 7 · 2026-04-12 08:38:44

661

Views

Prove that if every linear operator which commutes with $T$ is a polynomial in $T$, then $T$ admits a cyclic vector $v$ in $V$ (finite dimensional).

Published on 12 Apr 2026 - 8:38

score 219 · Answer 8 · 2026-04-10 00:26:58

219

Views

Constant term in a minimal polynomial is a scalar, but not so when polynomial is composed with linear transformation.

Published on 10 Apr 2026 - 0:26

score 869 · Answer 9 · 2026-04-08 20:47:48

869

Views

Minimal Polynomial of null operator

Published on 08 Apr 2026 - 20:47

score 60 · Answer 10 · 2026-04-11 11:16:18

60

Views

Linear transformation and minimal polynomial

Published on 11 Apr 2026 - 11:16

score 80 · Answer 11 · 2026-04-15 09:23:48

80

Views

Finding the incorrect statement out of these

Published on 15 Apr 2026 - 9:23

score 103 · Answer 12 · 2026-05-11 07:52:22

103

Views

If $(A + I_n)^m = 0$, show that $A$ is invertible and find $\det(A)$

Published on 11 May 2026 - 7:52

score 252 · Answer 13 · 2026-04-15 04:45:08

252

Views

Prove that the degree of the minimal polynomial over $\mathbb{Q}$ is a power of $2$

Published on 15 Apr 2026 - 4:45

score 294 · Answer 14 · 2026-04-11 16:38:13

294

Views

Minimal polynomial of operator with all eigenvalues are 1

Published on 11 Apr 2026 - 16:38

score 89 · Answer 15 · 2026-05-11 09:15:28

89

Views

The characteristic polynomial of S is $p(z)=(z−1)^2(z−2)^2$. What is the minimal polynomial of S?

Published on 11 May 2026 - 9:15

List Question

$A^3 = A^2$ How can $A$'s minimal polynomial look like?

Minimal polynomial for module over $A$ such that $A[x]$ is not a PID

Find minimal polynomial of matrix with some given property

Clarification Regarding to prove diagonalisable operator iff Minimal Polynomial Splits and

Show that $F(T)$ is invertible if and only if it has no common factors with the minimal polynomial of T.

Find the minimal polynomial over $\mathbb{Q}(i)$

Prove that if every linear operator which commutes with $T$ is a polynomial in $T$, then $T$ admits a cyclic vector $v$ in $V$ (finite dimensional).

Constant term in a minimal polynomial is a scalar, but not so when polynomial is composed with linear transformation.

Minimal Polynomial of null operator

Linear transformation and minimal polynomial

Finding the incorrect statement out of these

If $(A + I_n)^m = 0$, show that $A$ is invertible and find $\det(A)$

Prove that the degree of the minimal polynomial over $\mathbb{Q}$ is a power of $2$

Minimal polynomial of operator with all eigenvalues are 1

The characteristic polynomial of S is $p(z)=(z−1)^2(z−2)^2$. What is the minimal polynomial of S?

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