Question

Is a symmetric real matrix similar to a diagonal matrix through an orthogonal matrix?

score 450 · Answer 1 · 2026-03-26 01:10:45

450

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Is a symmetric real matrix similar to a diagonal matrix through an orthogonal matrix?

Published on 26 Mar 2026 - 1:10

score 244 · Answer 2 · 2021-06-21 19:13:20

244

Views

Show that a function is radial iff it is rotation invariant

Published on 21 Jun 2021 - 19:13

score 152 · Answer 3 · 2021-07-05 08:56:25

152

Views

Eigenvalue of an orthogonal matrix

Published on 05 Jul 2021 - 8:56

score 215 · Answer 4 · 2021-07-10 19:42:51

215

Views

Question about proof that $\det(Q)=\pm 1$ for orthogonal matrix $Q$

Published on 10 Jul 2021 - 19:42

score 1.8k · Answer 5 · 2021-07-11 12:06:43

1.8k

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Orthogonal projection using orthogonal matrices: $QQ^T\neq Q^TQ$

Published on 11 Jul 2021 - 12:06

score 382 · Answer 6 · 2021-07-12 10:11:49

382

Views

Is the "Its transpose is its inverse" definition of an orthogonal matrix equivalent to the "It preserves the dot product" definition?

Published on 12 Jul 2021 - 10:11

score 430 · Answer 7 · 2021-07-21 14:46:11

430

Views

Can orthogonal matrix with positive diagonal have -1 in its spectrum?

Published on 21 Jul 2021 - 14:46

score 173 · Answer 8 · 2021-07-23 04:17:40

173

Views

An inequality of eigenvalues of $A$ and $U^TAU$, where $A$ is symmetric, $U^TU = I$.

Published on 23 Jul 2021 - 4:17

score 177 · Answer 9 · 2021-07-23 14:07:10

177

Views

Prove that if $AA^{*}$ is Orthogonal $\Rightarrow$ A is Orthogonal. ($A\in\mathbb{R}_{nxn}$)

Published on 23 Jul 2021 - 14:07

score 262 · Answer 10 · 2021-08-08 08:23:41

262

Views

Understanding the loss of orthogonality of Classical Gram-Schmidt Procedure

Published on 08 Aug 2021 - 8:23

score 119 · Answer 11 · 2026-02-23 05:43:27

119

Views

How to construct Hadamard Matrices of size $3 \cdot 2^n $?

Published on 23 Feb 2026 - 5:43

score 57 · Answer 12 · 2021-08-16 10:44:35

57

Views

Scalarproduct with orthogonal matrices

Published on 16 Aug 2021 - 10:44

score 90 · Answer 13 · 2021-08-17 13:22:32

90

Views

Global parameterization of $SO(3, \mathbb R)$ with $3$ real numbers (showing $SO(3)$ is closed).

Published on 17 Aug 2021 - 13:22

score 217 · Answer 14 · 2021-08-18 06:33:58

217

Views

When is $||Ax||_2 \leq ||x||_2$ true for all $x$?

Published on 18 Aug 2021 - 6:33

score 985 · Answer 15 · 2021-08-21 07:07:08

985

Views

If $(Av,Au)=(v,u)$ then matrix $A$ is orthogonal

Published on 21 Aug 2021 - 7:07

List Question

Is a symmetric real matrix similar to a diagonal matrix through an orthogonal matrix?

Show that a function is radial iff it is rotation invariant

Eigenvalue of an orthogonal matrix

Question about proof that $\det(Q)=\pm 1$ for orthogonal matrix $Q$

Orthogonal projection using orthogonal matrices: $QQ^T\neq Q^TQ$

Is the "Its transpose is its inverse" definition of an orthogonal matrix equivalent to the "It preserves the dot product" definition?

Can orthogonal matrix with positive diagonal have -1 in its spectrum?

An inequality of eigenvalues of $A$ and $U^TAU$, where $A$ is symmetric, $U^TU = I$.

Prove that if $AA^{*}$ is Orthogonal $\Rightarrow$ A is Orthogonal. ($A\in\mathbb{R}_{nxn}$)

Understanding the loss of orthogonality of Classical Gram-Schmidt Procedure

How to construct Hadamard Matrices of size $3 \cdot 2^n $?

Scalarproduct with orthogonal matrices

Global parameterization of $SO(3, \mathbb R)$ with $3$ real numbers (showing $SO(3)$ is closed).

When is $||Ax||_2 \leq ||x||_2$ true for all $x$?

If $(Av,Au)=(v,u)$ then matrix $A$ is orthogonal

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