Question

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).

score 661 · Answer 1 · 2026-04-12 08:38:44

661

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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 1.2k · Answer 2 · 2026-04-11 21:21:20

1.2k

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Using Gram-Schmidt to find the QR decomposition

Published on 11 Apr 2026 - 21:21

score 49 · Answer 3 · 2026-04-13 04:56:18

49

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Eigenvalues of a particular block matrix

Published on 13 Apr 2026 - 4:56

score 70 · Answer 4 · 2026-04-09 08:15:47

70

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What are the steps to simplify this matrix?

Published on 09 Apr 2026 - 8:15

score 1.7k · Answer 5 · 2026-04-09 16:38:34

1.7k

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How to find a value for a variable that makes a matrix (with said variable) equal to its own inverse

Published on 09 Apr 2026 - 16:38

score 1.1k · Answer 6 · 2026-04-13 10:21:45

1.1k

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If $\det(A)\det(B) \ne 0$, are $A$ and $B$ are row equivalent?

Published on 13 Apr 2026 - 10:21

score 83 · Answer 7 · 2026-04-14 04:43:15

83

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Is $P\cdot S$ skew symmetric, if $S$ is skew symmetric and $P$ is symmetric positive definite?

Published on 14 Apr 2026 - 4:43

score 123 · Answer 8 · 2026-04-15 23:34:33

123

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Invertible matrix theorem

Published on 15 Apr 2026 - 23:34

score 1.6k · Answer 9 · 2026-04-13 14:11:11

1.6k

Views

Matrix Geometric Series

Published on 13 Apr 2026 - 14:11

score 213 · Answer 10 · 2026-04-12 10:26:06

213

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Does every continuous conjugation-invariant function factor through polynomials in the eigenvalues?

Published on 12 Apr 2026 - 10:26

score 48 · Answer 11 · 2026-04-15 13:18:30

48

Views

Why $Ax=e_i$ means $A$ can be reduced row echelon form?

Published on 15 Apr 2026 - 13:18

score 284 · Answer 12 · 2026-04-13 22:23:38

284

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Find the ideals of $M_2(\mathbb{Z}_{12})$ and find their orders.

Published on 13 Apr 2026 - 22:23

score 65 · Answer 13 · 2026-04-16 13:09:56

65

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The $m$-order submatrixs respectively from two $m\times n$ matrixs

Published on 16 Apr 2026 - 13:09

score 221 · Answer 14 · 2026-04-11 00:55:36

221

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How to change the base cases of a tribonacci sequence solved by matrix exponentation

Published on 11 Apr 2026 - 0:55

score 2k · Answer 15 · 2026-03-26 01:07:39

2k

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Rank comparison for different low rank approximations

Published on 26 Mar 2026 - 1:07

List Question

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).

Using Gram-Schmidt to find the QR decomposition

Eigenvalues of a particular block matrix

What are the steps to simplify this matrix?

How to find a value for a variable that makes a matrix (with said variable) equal to its own inverse

If $\det(A)\det(B) \ne 0$, are $A$ and $B$ are row equivalent?

Is $P\cdot S$ skew symmetric, if $S$ is skew symmetric and $P$ is symmetric positive definite?

Invertible matrix theorem

Matrix Geometric Series

Does every continuous conjugation-invariant function factor through polynomials in the eigenvalues?

Why $Ax=e_i$ means $A$ can be reduced row echelon form?

Find the ideals of $M_2(\mathbb{Z}_{12})$ and find their orders.

The $m$-order submatrixs respectively from two $m\times n$ matrixs

How to change the base cases of a tribonacci sequence solved by matrix exponentation

Rank comparison for different low rank approximations

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