Question

Show that a 2x2 matrix A with complex eigenvalues has a special similarity

score 1.9k · Answer 1 · 2019-04-20 06:20:41

1.9k

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Show that a 2x2 matrix A with complex eigenvalues has a special similarity

Published on 20 Apr 2019 - 6:20

score 608 · Answer 2 · 2019-04-20 08:30:37

608

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Let $T$ be a linear operator on a finite-dimensional vector space, $f$ is any polynomial, find out the relation between eigenvalues of $f(T)$ and $T$.

Published on 20 Apr 2019 - 8:30

score 91 · Answer 3 · 2019-04-20 12:40:06

91

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Derivative of eigenvalue with respect to a constant

Published on 20 Apr 2019 - 12:40

score 3k · Answer 4 · 2019-04-20 23:52:17

3k

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The eigenspace of $\lambda$ is simply the null space of the matrix $A-\lambda I$. Is that correct?

Published on 20 Apr 2019 - 23:52

score 449 · Answer 5 · 2019-04-21 00:05:12

449

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Why does invertibility of the matrix $A-\lambda I$ imply that $\lambda$ is not an eigenvalue?

Published on 21 Apr 2019 - 0:05

score 160 · Answer 6 · 2026-03-25 23:10:43

160

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Rank-1 modification of correlation matrix

Published on 25 Mar 2026 - 23:10

score 340 · Answer 7 · 2026-03-26 07:35:40

340

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Question of the Cholesky decomposition of symmetric positive definite matrix

Published on 26 Mar 2026 - 7:35

score 227 · Answer 8 · 2019-04-22 12:45:09

227

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Finding the characteristic polynomial of the $T: \mathcal{M}_{n} (\mathbb{R}) \to \mathcal{M}_{n} (\mathbb{R})$ given by $T(M)=M^{\text{tr}}$

Published on 22 Apr 2019 - 12:45

score 98 · Answer 9 · 2019-04-22 16:12:11

98

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Given $R$ and its eigenvalues, find the eigenvalues of $R + 2I$:

Published on 22 Apr 2019 - 16:12

score 288 · Answer 10 · 2026-03-27 04:22:41

288

Views

How to use eigenvalues and eigenvectors to compute $A^{1000}$

Published on 27 Mar 2026 - 4:22

score 45 · Answer 11 · 2019-04-23 16:43:29

45

Views

linear algebra eigenvalue proof question

Published on 23 Apr 2019 - 16:43

score 170 · Answer 12 · 2019-04-23 17:17:10

170

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Degenerate eigenvalues and finding normalized eigenvectors

Published on 23 Apr 2019 - 17:17

score 1.1k · Answer 13 · 2026-03-27 10:09:32

1.1k

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Find orthogonal basis for 3x3 Symmetric Matrix

Published on 27 Mar 2026 - 10:09

score 2.3k · Answer 14 · 2026-03-25 16:33:23

2.3k

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Are these square matrices always diagonalisable?

Published on 25 Mar 2026 - 16:33

score 41 · Answer 15 · 2026-03-28 09:45:29

41

Views

How do the values of $a$ affect definiteness of this matrix $\textbf{A}$?

Published on 28 Mar 2026 - 9:45

List Question

Show that a 2x2 matrix A with complex eigenvalues has a special similarity

Let $T$ be a linear operator on a finite-dimensional vector space, $f$ is any polynomial, find out the relation between eigenvalues of $f(T)$ and $T$.

Derivative of eigenvalue with respect to a constant

The eigenspace of $\lambda$ is simply the null space of the matrix $A-\lambda I$. Is that correct?

Why does invertibility of the matrix $A-\lambda I$ imply that $\lambda$ is not an eigenvalue?

Rank-1 modification of correlation matrix

Question of the Cholesky decomposition of symmetric positive definite matrix

Finding the characteristic polynomial of the $T: \mathcal{M}_{n} (\mathbb{R}) \to \mathcal{M}_{n} (\mathbb{R})$ given by $T(M)=M^{\text{tr}}$

Given $R$ and its eigenvalues, find the eigenvalues of $R + 2I$:

How to use eigenvalues and eigenvectors to compute $A^{1000}$

linear algebra eigenvalue proof question

Degenerate eigenvalues and finding normalized eigenvectors

Find orthogonal basis for 3x3 Symmetric Matrix

Are these square matrices always diagonalisable?

How do the values of $a$ affect definiteness of this matrix $\textbf{A}$?

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