Question

When is an invertible $n \times n$ matrix (over an arbitrary ring) similar to its inverse?

score 258 · Answer 1 · 2021-08-19 07:09:10

258

Views

When is an invertible $n \times n$ matrix (over an arbitrary ring) similar to its inverse?

Published on 19 Aug 2021 - 7:09

score 1.7k · Answer 2 · 2021-08-24 06:00:09

1.7k

Views

Counting the number of similar matrices over finite fields

Published on 24 Aug 2021 - 6:00

score 90 · Answer 3 · 2021-09-09 07:53:46

90

Views

A question related to similarity of a Complex matrix that is not scalar multiple of $I_n$

Published on 09 Sep 2021 - 7:53

score 60 · Answer 4 · 2021-09-22 20:44:29

60

Views

If A and B are both diagonalizable to another matrix C, is A similar to B?

Published on 22 Sep 2021 - 20:44

score 184 · Answer 5 · 2021-10-12 15:01:35

184

Views

Nilpotent matrix and similar matrix

Published on 12 Oct 2021 - 15:01

score 400 · Answer 6 · 2021-10-13 18:43:51

400

Views

When do similarity transformations preserve Hermitianity?

Published on 13 Oct 2021 - 18:43

score 61 · Answer 7 · 2026-03-25 08:09:43

61

Views

Prove the existence of a similar matrix

Published on 25 Mar 2026 - 8:09

score 123 · Answer 8 · 2026-03-25 04:40:30

123

Views

Show that every matrix with real eigenvalue less than $0$ is similar to dissipative matrix

Published on 25 Mar 2026 - 4:40

score 56 · Answer 9 · 2021-11-08 15:30:48

56

Views

The result of two change of basis is the same. Then the bases must be the same?

Published on 08 Nov 2021 - 15:30

score 45 · Answer 10 · 2021-11-09 09:26:21

45

Views

finding the matrix for this linear transformation: "x-y, -x+3y" (in R2; it's an endomorphism)

Published on 09 Nov 2021 - 9:26

score 100 · Answer 11 · 2021-11-10 12:04:21

100

Views

What's the name of the transformation from a matrix $M$ to $A M A^T$?

Published on 10 Nov 2021 - 12:04

score 254 · Answer 12 · 2021-11-15 07:15:53

254

Views

Similarity transformation of an orthogonal matrix

Published on 15 Nov 2021 - 7:15

score 390 · Answer 13 · 2021-11-19 20:40:50

390

Views

Let A be an n × n orthogonal matrix. Either prove or disprove that any matrix similar to A is also orthogonal.

Published on 19 Nov 2021 - 20:40

score 67 · Answer 14 · 2021-12-07 04:01:26

67

Views

Determine if complex matrices are similar

Published on 07 Dec 2021 - 4:01

score 255 · Answer 15 · 2026-03-25 21:22:56

255

Views

Proving that every symmetric matrix is similar to a symmetric tridiagonal matrix

Published on 25 Mar 2026 - 21:22

List Question

When is an invertible $n \times n$ matrix (over an arbitrary ring) similar to its inverse?

Counting the number of similar matrices over finite fields

A question related to similarity of a Complex matrix that is not scalar multiple of $I_n$

If A and B are both diagonalizable to another matrix C, is A similar to B?

Nilpotent matrix and similar matrix

When do similarity transformations preserve Hermitianity?

Prove the existence of a similar matrix

Show that every matrix with real eigenvalue less than $0$ is similar to dissipative matrix

The result of two change of basis is the same. Then the bases must be the same?

finding the matrix for this linear transformation: "x-y, -x+3y" (in R2; it's an endomorphism)

What's the name of the transformation from a matrix $M$ to $A M A^T$?

Similarity transformation of an orthogonal matrix

Let A be an n × n orthogonal matrix. Either prove or disprove that any matrix similar to A is also orthogonal.

Determine if complex matrices are similar

Proving that every symmetric matrix is similar to a symmetric tridiagonal matrix

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