List questions from orthogonal-matrices

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Is $O(k)\times O(n-k)$ closed in $SO(n)$?

Published on 24 Mar 2026 - 18:18

130

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projector on the boundary of a simplex. aka find basis for subspace $\sum_j x_j=0$.

Published on 25 Mar 2026 - 10:43

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Derivative w.r.t orthogonal matrix

Published on 25 Mar 2026 - 1:24

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Show that the eigenvalues of $\mathcal{O}(n,\mathbb{R})$ have magnitude 1.

Published on 24 Mar 2026 - 23:46

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Find all possible values of $p$, $q$ and $r$ such that this matrix is orthogonal

Published on 10 Mar 2018 - 17:24

64

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Let $H$ be the set of matrices in $O_n(\mathbb{R})$ whose matrix entries are integers.

Published on 12 Mar 2018 - 3:56

53

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Help in proving linear algebra about inverse of a symmetric matrix

Published on 25 Mar 2026 - 8:10

189

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Rotationally Invariance Of Probability Density Functions

Published on 25 Mar 2026 - 1:26

1.6k

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Prove $O(2)$ is non-abelian?

Published on 17 Mar 2026 - 3:48

143

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Dot product over upper matrix and matrix of units

Published on 17 Mar 2026 - 11:35

178

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How many matrices does SO(2) contain?

Published on 17 Mar 2026 - 2:44

452

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Matrix Representation of Rotation in $\mathbb{R^3}$

Published on 17 Mar 2026 - 9:16

1.2k

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Prove that if $M$ is orthogonal, then $\det(M)= \pm 1$

Published on 17 Mar 2026 - 22:38

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How to prove the complement $P^\perp$ of a projection matrix $P$ have relation $I-P=P^\perp$

Published on 03 Apr 2018 - 7:22

List Question

Why is $O(n)$ compact?

Is $O(k)\times O(n-k)$ closed in $SO(n)$?

projector on the boundary of a simplex. aka find basis for subspace $\sum_j x_j=0$.

Derivative w.r.t orthogonal matrix

Show that the eigenvalues of $\mathcal{O}(n,\mathbb{R})$ have magnitude 1.

Find all possible values of $p$, $q$ and $r$ such that this matrix is orthogonal

Let $H$ be the set of matrices in $O_n(\mathbb{R})$ whose matrix entries are integers.

Help in proving linear algebra about inverse of a symmetric matrix

Rotationally Invariance Of Probability Density Functions

Prove $O(2)$ is non-abelian?

Dot product over upper matrix and matrix of units

How many matrices does SO(2) contain?

Matrix Representation of Rotation in $\mathbb{R^3}$

Prove that if $M$ is orthogonal, then $\det(M)= \pm 1$

How to prove the complement $P^\perp$ of a projection matrix $P$ have relation $I-P=P^\perp$

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