Question

Let $\alpha, \beta,\gamma,\delta $ be the eigenvalues of the matrix find $\alpha ^2+\beta^2+\gamma^2+\delta^2 $

score 3k · Answer 1 · 2019-01-25 05:10:32

3k

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Let $\alpha, \beta,\gamma,\delta $ be the eigenvalues of the matrix find $\alpha ^2+\beta^2+\gamma^2+\delta^2 $

Published on 25 Jan 2019 - 5:10

score 64 · Answer 2 · 2026-03-26 14:19:51

64

Views

Show that $A = \sum_i \lambda_i x_i x_i^T$

Published on 26 Mar 2026 - 14:19

score 216 · Answer 3 · 2026-03-27 06:44:20

216

Views

Construct operator with given spectrum.

Published on 27 Mar 2026 - 6:44

score 791 · Answer 4 · 2019-01-25 19:56:38

791

Views

Is there an explicit relationship between the eigenvalues of a matrix and its derivative?

Published on 25 Jan 2019 - 19:56

score 1.2k · Answer 5 · 2026-03-26 14:21:05

1.2k

Views

Decomposition of matrix into sum of product of vectors

Published on 26 Mar 2026 - 14:21

score 1.1k · Answer 6 · 2019-01-27 01:18:23

1.1k

Views

If $A$ be a matrix with $n$ distinct eigenvalues then $u, Au , A^2u ,\cdots, A^{n-1} u$ will be independent.

Published on 27 Jan 2019 - 1:18

score 107 · Answer 7 · 2019-01-27 09:48:01

107

Views

Show that $\dim E_\lambda (A^TA) = \dim E_\lambda (AA^T)$.

Published on 27 Jan 2019 - 9:48

score 100 · Answer 8 · 2019-01-27 11:04:06

100

Views

Spectral Radius proof

Published on 27 Jan 2019 - 11:04

score 70 · Answer 9 · 2026-03-28 22:27:06

70

Views

Expected number of rounds in a game based on chance

Published on 28 Mar 2026 - 22:27

score 70 · Answer 10 · 2019-01-27 15:44:12

70

Views

Find subspace $T$ of $M_{2x2} (\mathbb{R})$ such that eigenvector is $\begin{bmatrix} 1\\ 2 \end{bmatrix}$

Published on 27 Jan 2019 - 15:44

score 40 · Answer 11 · 2026-03-26 14:19:53

40

Views

$\mathbf{A}\mathbf{X} = \mathbf{X}\mathbf{M}$ implies eigenvalues of $\mathbf{M}$ are eigenvalues of $\mathbf{A}$

Published on 26 Mar 2026 - 14:19

score 207 · Answer 12 · 2026-03-27 05:54:58

207

Views

Show vector is approximately an eigenvector of matrix, thus find eigenvalue

Published on 27 Mar 2026 - 5:54

score 188 · Answer 13 · 2019-01-28 20:31:44

188

Views

How to prove that eigenvalues of a symmetric matrix with respect to a metric are real, and that there always exists an eigenbasis?

Published on 28 Jan 2019 - 20:31

score 213 · Answer 14 · 2026-03-25 13:55:16

213

Views

Relation between eigenvectors and powers of a matrix for finding out if a graph is disconnected

Published on 25 Mar 2026 - 13:55

score 198 · Answer 15 · 2026-04-01 22:14:08

198

Views

Do two unitary operators that commute have same eigenvalues?

Published on 01 Apr 2026 - 22:14

List Question

Let $\alpha, \beta,\gamma,\delta $ be the eigenvalues of the matrix find $\alpha ^2+\beta^2+\gamma^2+\delta^2 $

Show that $A = \sum_i \lambda_i x_i x_i^T$

Construct operator with given spectrum.

Is there an explicit relationship between the eigenvalues of a matrix and its derivative?

Decomposition of matrix into sum of product of vectors

If $A$ be a matrix with $n$ distinct eigenvalues then $u, Au , A^2u ,\cdots, A^{n-1} u$ will be independent.

Show that $\dim E_\lambda (A^TA) = \dim E_\lambda (AA^T)$.

Spectral Radius proof

Expected number of rounds in a game based on chance

Find subspace $T$ of $M_{2x2} (\mathbb{R})$ such that eigenvector is $\begin{bmatrix} 1\\ 2 \end{bmatrix}$

$\mathbf{A}\mathbf{X} = \mathbf{X}\mathbf{M}$ implies eigenvalues of $\mathbf{M}$ are eigenvalues of $\mathbf{A}$

Show vector is approximately an eigenvector of matrix, thus find eigenvalue

How to prove that eigenvalues of a symmetric matrix with respect to a metric are real, and that there always exists an eigenbasis?

Relation between eigenvectors and powers of a matrix for finding out if a graph is disconnected

Do two unitary operators that commute have same eigenvalues?

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