Question

Show that if $A \in M_{2 \times 2}(\mathbb{R})$ then $A, A^T$ are similar.

score 193 · Answer 1 · 2023-12-26 11:40:41

193

Views

Show that if $A \in M_{2 \times 2}(\mathbb{R})$ then $A, A^T$ are similar.

Published on 26 Dec 2023 - 11:40

score 105 · Answer 2 · 2024-01-16 22:35:19

105

Views

Does similarity of matrices preserve sum of principal minors?

Published on 16 Jan 2024 - 22:35

score 118 · Answer 3 · 2024-01-17 09:50:09

118

Views

If characteristic polynomial of $A$ is $(x-1)^n$, then show $A$ and $A^{-1}$ are similar

Published on 17 Jan 2024 - 9:50

score 45 · Answer 4 · 2024-01-18 04:08:48

45

Views

$A,B,A_1,B_1$ are $n\times n$ matrices, $A\sim A_1, B\sim B_1$, $n$ is odd, $AB=0$, show that at least one of $A+A_1,B+B_1$ is singular.

Published on 18 Jan 2024 - 4:08

score 145 · Answer 5 · 2024-01-19 16:31:58

145

Views

Are two diagonals with equal spectra similar to each other?

Published on 19 Jan 2024 - 16:31

score 27 · Answer 6 · 2024-02-15 15:21:21

27

Views

Find the change of basis matrix so that the following is in Jordan Normal Form

Published on 15 Feb 2024 - 15:21

score 51 · Answer 7 · 2024-02-24 12:44:11

51

Views

Any singular matrix is similar to a matrix of form $\begin{pmatrix}B&\\&0\end{pmatrix}$

Published on 24 Feb 2024 - 12:44

score 38 · Answer 8 · 2024-03-10 16:56:38

38

Views

Is this basis for complex matrices necessarily a unitary basis?

Published on 10 Mar 2024 - 16:56

score 191 · Answer 9 · 2024-03-26 20:50:47

191

Views

In what sense are similar matrices "the same," and how can this be generalized?

Published on 26 Mar 2024 - 20:50

score 595 · Answer 10 · 2015-01-12 13:34:46

595

Views

why similarity over $\bar{\mathbb{F}}$ of $A,B\in M_n(\mathbb{F})$ implies similarity over $\mathbb{F}$?

Published on 12 Jan 2015 - 13:34

score 19.2k · Answer 11 · 2015-06-24 13:20:36

19.2k

Views

Why do similar matrices have the same rank?

Published on 24 Jun 2015 - 13:20

score 2k · Answer 12 · 2015-12-15 21:17:48

2k

Views

How to prove two diagonalizable matrices are similar iff they have same eigenvalue with same multiplicity?

Published on 15 Dec 2015 - 21:17

score 2k · Answer 13 · 2013-05-10 17:56:01

2k

Views

If the matrix is positive definite, then its similar matrix is also positive definite?

Published on 10 May 2013 - 17:56

score 703 · Answer 14 · 2013-06-02 20:34:16

703

Views

Matrix similar to a companion matrix

Published on 02 Jun 2013 - 20:34

score 1.1k · Answer 15 · 2013-09-01 00:42:01

1.1k

Views

What can we say about two graphs if they have similar adjacency matrices?

Published on 01 Sep 2013 - 0:42

List Question

Show that if $A \in M_{2 \times 2}(\mathbb{R})$ then $A, A^T$ are similar.

Does similarity of matrices preserve sum of principal minors?

If characteristic polynomial of $A$ is $(x-1)^n$, then show $A$ and $A^{-1}$ are similar

$A,B,A_1,B_1$ are $n\times n$ matrices, $A\sim A_1, B\sim B_1$, $n$ is odd, $AB=0$, show that at least one of $A+A_1,B+B_1$ is singular.

Are two diagonals with equal spectra similar to each other?

Find the change of basis matrix so that the following is in Jordan Normal Form

Any singular matrix is similar to a matrix of form $\begin{pmatrix}B&\\&0\end{pmatrix}$

Is this basis for complex matrices necessarily a unitary basis?

In what sense are similar matrices "the same," and how can this be generalized?

why similarity over $\bar{\mathbb{F}}$ of $A,B\in M_n(\mathbb{F})$ implies similarity over $\mathbb{F}$?

Why do similar matrices have the same rank?

How to prove two diagonalizable matrices are similar iff they have same eigenvalue with same multiplicity?

If the matrix is positive definite, then its similar matrix is also positive definite?

Matrix similar to a companion matrix

What can we say about two graphs if they have similar adjacency matrices?

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