Question

A continous extension of the group of permutation matrices

score 90 · Answer 1 · 2026-03-26 04:34:12

90

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A continous extension of the group of permutation matrices

Published on 26 Mar 2026 - 4:34

score 63 · Answer 2 · 2026-03-29 07:22:23

63

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Show that $U^tWU \sim W$

Published on 29 Mar 2026 - 7:22

score 126 · Answer 3 · 2020-08-06 13:05:49

126

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Can an orthogonal matrix that represents a linear transformation from $\mathbb{R}^n \to \mathbb{R}^n$ have no eigenvalues?

Published on 06 Aug 2020 - 13:05

score 94 · Answer 4 · 2026-03-25 22:05:23

94

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If $ A $ is a $ 2 \times 2 $ real matrix such that $ \det (A) = 1 $ and $ A^n = I$ show that $ A ^tA = I $

Published on 25 Mar 2026 - 22:05

score 273 · Answer 5 · 2020-08-08 03:53:13

273

Views

Let A be a real $m \times n$ matrix. Prove that there are orthogonal matrices $P,Q$ such that $PAQ$ is diagonal, with non-negative diagonal entries.

Published on 08 Aug 2020 - 3:53

score 110 · Answer 6 · 2026-03-25 14:24:38

110

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Show that the group operation of conjugation is compatible with the bilinear form $\langle A,B\rangle=1/2 \textrm{ trace }AB$

Published on 25 Mar 2026 - 14:24

score 41 · Answer 7 · 2026-03-28 03:32:53

41

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Theorem deduction using Orthonormal Projections Matrix

Published on 28 Mar 2026 - 3:32

score 212 · Answer 8 · 2026-03-25 21:01:38

212

Views

Show that: if $Cond_2(A)=1$ then $A=\alpha Q$; where $Q $ is an orthonormal matrix and $\alpha$ is a real number $\neq 0$

Published on 25 Mar 2026 - 21:01

score 199 · Answer 9 · 2026-03-25 17:44:40

199

Views

$A$ is real matrix and for some $k\geq 2,A^{k}$ is similar to an orthogonal matrix,how to prove $A$ is also similar to an orthogonal matrix?

Published on 25 Mar 2026 - 17:44

score 122 · Answer 10 · 2020-08-18 04:03:28

122

Views

How to write an orthogonal matrix as multiplication of two orthogonal and symmetric matrix?

Published on 18 Aug 2020 - 4:03

score 1k · Answer 11 · 2020-08-18 04:28:48

1k

Views

Complex Matrix is Orthogonal if and only if...

Published on 18 Aug 2020 - 4:28

score 112 · Answer 12 · 2020-08-19 17:06:01

112

Views

Is it possible to find an orthogonal matrix $V\in M_n(\Bbb R)$ s. t. $A=VDV^T$ with a column not proportional to any column of $U$?

Published on 19 Aug 2020 - 17:06

score 33 · Answer 13 · 2020-08-20 10:48:37

33

Views

Orthogonal matrix and Froebenius norm

Published on 20 Aug 2020 - 10:48

score 166 · Answer 14 · 2020-08-21 18:29:58

166

Views

A linear transfomation $h:\Bbb R^n\rightarrow\Bbb R^n$ is orthogonal iff carries a base $\mathcal V$ in an orthonormal base $\mathcal V'$.

Published on 21 Aug 2020 - 18:29

score 528 · Answer 15 · 2020-08-24 22:05:16

528

Views

Orthogonal Basis Vectors

Published on 24 Aug 2020 - 22:05

List Question

A continous extension of the group of permutation matrices

Show that $U^tWU \sim W$

Can an orthogonal matrix that represents a linear transformation from $\mathbb{R}^n \to \mathbb{R}^n$ have no eigenvalues?

If $ A $ is a $ 2 \times 2 $ real matrix such that $ \det (A) = 1 $ and $ A^n = I$ show that $ A ^tA = I $

Let A be a real $m \times n$ matrix. Prove that there are orthogonal matrices $P,Q$ such that $PAQ$ is diagonal, with non-negative diagonal entries.

Show that the group operation of conjugation is compatible with the bilinear form $\langle A,B\rangle=1/2 \textrm{ trace }AB$

Theorem deduction using Orthonormal Projections Matrix

Show that: if $Cond_2(A)=1$ then $A=\alpha Q$; where $Q $ is an orthonormal matrix and $\alpha$ is a real number $\neq 0$

$A$ is real matrix and for some $k\geq 2,A^{k}$ is similar to an orthogonal matrix,how to prove $A$ is also similar to an orthogonal matrix?

How to write an orthogonal matrix as multiplication of two orthogonal and symmetric matrix?

Complex Matrix is Orthogonal if and only if...

Is it possible to find an orthogonal matrix $V\in M_n(\Bbb R)$ s. t. $A=VDV^T$ with a column not proportional to any column of $U$?

Orthogonal matrix and Froebenius norm

A linear transfomation $h:\Bbb R^n\rightarrow\Bbb R^n$ is orthogonal iff carries a base $\mathcal V$ in an orthonormal base $\mathcal V'$.

Orthogonal Basis Vectors

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