Question

Restriction of a diagonalizable linear operator $T$ to any nontrivial $T$-invariant subspace is also diagonalizable using a given lemma.

score 1.5k · Answer 1 · 2026-03-25 06:12:12

1.5k

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Restriction of a diagonalizable linear operator $T$ to any nontrivial $T$-invariant subspace is also diagonalizable using a given lemma.

Published on 25 Mar 2026 - 6:12

score 67 · Answer 2 · 2018-06-04 07:13:59

67

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How to find $3 \times 3$ matrix from $2$ given eigenvalues and respective eigenvectors?

Published on 04 Jun 2018 - 7:13

score 75 · Answer 3 · 2018-06-04 15:39:48

How to prove, for any vector $v$ and matrix $A$, $\langle Av,v\rangle\le \lambda\langle v,v\rangle$, where $\lambda$ is the maximum eigenvalue of $A$

score 101 · Answer 4 · 2018-06-05 02:47:25

101

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The dimension of the eigenvector space of irreducible matrix

Published on 05 Jun 2018 - 2:47

score 106 · Answer 5 · 2026-03-22 11:30:22

106

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Equivalent variational formula for eigenvalues

Published on 22 Mar 2026 - 11:30

score 575 · Answer 6 · 2026-03-29 16:24:24

575

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Eigenvalues of a permutation operator in $\mathbb{C}^n$

Published on 29 Mar 2026 - 16:24

score 42 · Answer 7 · 2026-03-25 11:17:40

42

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Determining whether a matrix is unitary when given its eigenspaces

Published on 25 Mar 2026 - 11:17

score 296 · Answer 8 · 2026-03-27 14:21:18

296

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Finding the pattern to a general matrix

Published on 27 Mar 2026 - 14:21

score 140 · Answer 9 · 2026-03-25 07:43:55

140

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Without Calculation, why is $Q^{-1}$ a Matrix of Rotation

Published on 25 Mar 2026 - 7:43

score 128 · Answer 10 · 2026-03-30 11:04:09

128

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Assume T is an operator on a finite dimensional real vector space and all the eigen values are real. Prove that Tr($T^2$) $\ge 0$.

Published on 30 Mar 2026 - 11:04

score 63 · Answer 11 · 2018-06-07 11:47:56

63

Views

Can we always find an invertible matrix from a non-invertible one

Published on 07 Jun 2018 - 11:47

score 39 · Answer 12 · 2026-03-25 09:26:18

39

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If a matrix is positive-definite, is every term in its determinant (as sum over permutations) nonnegative?

Published on 25 Mar 2026 - 9:26

score 1k · Answer 13 · 2026-03-25 09:38:07

1k

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Relation between the maximum eigenvalues of symmetric positive definite matrix $A$ and $B A B^\dagger$

Published on 25 Mar 2026 - 9:38

score 2.7k · Answer 14 · 2026-03-24 07:31:47

2.7k

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Why does every symplectic matrix $M\in{\rm Sp}(2n,{\Bbb R})$ admit a symplectic eigenbasis?

Published on 24 Mar 2026 - 7:31

score 606 · Answer 15 · 2018-06-08 18:26:20

606

Views

Choosing an initial vector for the power rule.

Published on 08 Jun 2018 - 18:26

List Question

Restriction of a diagonalizable linear operator $T$ to any nontrivial $T$-invariant subspace is also diagonalizable using a given lemma.

How to find $3 \times 3$ matrix from $2$ given eigenvalues and respective eigenvectors?

How to prove, for any vector $v$ and matrix $A$, $\langle Av,v\rangle\le \lambda\langle v,v\rangle$, where $\lambda$ is the maximum eigenvalue of $A$

The dimension of the eigenvector space of irreducible matrix

Equivalent variational formula for eigenvalues

Eigenvalues of a permutation operator in $\mathbb{C}^n$

Determining whether a matrix is unitary when given its eigenspaces

Finding the pattern to a general matrix

Without Calculation, why is $Q^{-1}$ a Matrix of Rotation

Assume T is an operator on a finite dimensional real vector space and all the eigen values are real. Prove that Tr($T^2$) $\ge 0$.

Can we always find an invertible matrix from a non-invertible one

If a matrix is positive-definite, is every term in its determinant (as sum over permutations) nonnegative?

Relation between the maximum eigenvalues of symmetric positive definite matrix $A$ and $B A B^\dagger$

Why does every symplectic matrix $M\in{\rm Sp}(2n,{\Bbb R})$ admit a symplectic eigenbasis?

Choosing an initial vector for the power rule.

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