List questions from orthogonal-matrices

Published on 25 Mar 2026 - 22:30

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On two equivalent definitions of orthogonal matrix.

Published on 25 Sep 2019 - 15:39

28.6k

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What can be said about a matrix which is both symmetric and orthogonal?

Published on 16 Jun 2014 - 8:12

1.5k

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Determinant of identity minus product of orthogonal matrix and rank-$1$ matrix

Published on 19 Jul 2014 - 16:23

295

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What is "cyclic shift unitary" on $M_{n}(\mathbb{C})$?

Published on 25 Mar 2026 - 3:00

192

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Relation between different orthogonal groups

Published on 03 Oct 2019 - 21:30

53

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Is the matrix of this transformation orthogonal?

Published on 04 Oct 2019 - 20:55

112

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Is random homomorphism from free product of $k$ copies of $\mathbb Z_2$ to orthogonal group $O(3)$ injective?

Published on 25 Mar 2026 - 9:50

164

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$M$ is a $n\times n$ orthogonal matrix and has eigenvalues can have either $1$ or $-1$. Show that $M$ is diagonalizable

Published on 07 Oct 2019 - 22:03

47

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How can I solve a matrix $x^\top\!Mx=0$ with a better method?

Published on 09 Oct 2019 - 23:54

53

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Operations with orthogonal matrices

Published on 11 Oct 2019 - 5:26

1.3k

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Projection onto the tangent spaces of $O(n)$

Published on 12 Oct 2019 - 19:20

709

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Subgroup of O(2) isomorphic to $D_n$, matrices that form that group.

Published on 14 Oct 2019 - 5:26

200

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If the determinant of an real orthogonal matrix $Q$ is 1, prove that there exists a real skew-symmetric $K$ such that $Q=e^K$.

Published on 16 Oct 2019 - 8:17

528

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Quaternions and $SU(2)$

Published on 26 Mar 2026 - 5:36

List Question

Angle definition for $\text{SO}(3)$ matrices

On two equivalent definitions of orthogonal matrix.

What can be said about a matrix which is both symmetric and orthogonal?

Determinant of identity minus product of orthogonal matrix and rank-$1$ matrix

What is "cyclic shift unitary" on $M_{n}(\mathbb{C})$?

Relation between different orthogonal groups

Is the matrix of this transformation orthogonal?

Is random homomorphism from free product of $k$ copies of $\mathbb Z_2$ to orthogonal group $O(3)$ injective?

$M$ is a $n\times n$ orthogonal matrix and has eigenvalues can have either $1$ or $-1$. Show that $M$ is diagonalizable

How can I solve a matrix $x^\top\!Mx=0$ with a better method?

Operations with orthogonal matrices

Projection onto the tangent spaces of $O(n)$

Subgroup of O(2) isomorphic to $D_n$, matrices that form that group.

If the determinant of an real orthogonal matrix $Q$ is 1, prove that there exists a real skew-symmetric $K$ such that $Q=e^K$.

Quaternions and $SU(2)$

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