Question

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

score 194 · Answer 1 · 2026-03-25 14:36:51

194

Views

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

Published on 25 Mar 2026 - 14:36

score 106 · Answer 2 · 2026-03-25 14:36:43

106

Views

Does similarity of matrices preserve sum of principal minors?

Published on 25 Mar 2026 - 14:36

score 119 · Answer 3 · 2026-03-25 14:35:54

119

Views

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

Published on 25 Mar 2026 - 14:35

score 46 · Answer 4 · 2026-03-25 14:35:51

46

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 25 Mar 2026 - 14:35

score 146 · Answer 5 · 2026-03-25 14:34:33

146

Views

Are two diagonals with equal spectra similar to each other?

Published on 25 Mar 2026 - 14:34

score 28 · Answer 6 · 2026-03-25 14:36:45

28

Views

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

Published on 25 Mar 2026 - 14:36

score 52 · Answer 7 · 2026-03-25 14:34:38

52

Views

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

Published on 25 Mar 2026 - 14:34

score 39 · Answer 8 · 2026-03-25 14:29:57

39

Views

Is this basis for complex matrices necessarily a unitary basis?

Published on 25 Mar 2026 - 14:29

score 192 · Answer 9 · 2026-03-25 14:33:37

192

Views

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

Published on 25 Mar 2026 - 14:33

score 596 · Answer 10 · 2026-03-25 14:36:43

596

Views

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

Published on 25 Mar 2026 - 14:36

score 19.2k · Answer 11 · 2026-03-25 14:29:22

19.2k

Views

Why do similar matrices have the same rank?

Published on 25 Mar 2026 - 14:29

score 2k · Answer 12 · 2026-05-04 13:51:44

2k

Views

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

Published on 04 May 2026 - 13:51

score 2k · Answer 13 · 2026-03-25 14:34:39

2k

Views

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

Published on 25 Mar 2026 - 14:34

score 705 · Answer 14 · 2026-05-10 17:13:34

705

Views

Matrix similar to a companion matrix

Published on 10 May 2026 - 17:13

score 1.1k · Answer 15 · 2026-03-25 14:34:34

1.1k

Views

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

Published on 25 Mar 2026 - 14:34

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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