List questions from orthogonal-matrices

Published on 09 Apr 2026 - 17:31

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Left cosets complex orthogonal group under real orthogonal group

Published on 10 May 2026 - 15:08

28

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Property of $Q$ such that $\frac{x^TQx}{\|x\|^2} = \text{const}, \ \ \ \forall x\in \mathbb{R}^n$

Published on 16 Apr 2026 - 7:26

122

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Can a linear isometry always be expressed in terms of an orthogonal matrix?

Published on 10 Apr 2026 - 17:06

304

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Show that there is an orthogonal matrix $O$ such that $OA_1=A_2O$.

Published on 14 Apr 2026 - 22:32

126

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Show that $L_A$ acts on by orthogonal transformation and in particular rotation.

Published on 11 Apr 2026 - 3:06

120

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Orthogonal transformation with additional constraints

Published on 11 Apr 2026 - 4:58

123

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Minimizing Frobenius norm of the difference between $A$ and $P^\top B P$

Published on 13 Apr 2026 - 1:42

98

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Basis of an Orthogonal Complement

Published on 14 Apr 2026 - 8:55

256

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If $A$ has orthonormal columns then $||Ax||^2_2 = ||x||^2_2$, why?

Published on 13 Apr 2026 - 20:52

62

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Is the orthogonal polar factor the unique retraction $\operatorname{GL}_n^+ \to \operatorname{SO}_n$?

Published on 09 Apr 2026 - 6:21

1k

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Which matrices commute with $\operatorname{SO}_n$?

Published on 16 Apr 2026 - 16:42

1k

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How can we decompose the identity matrix given a set of orthonormal vectors?

Published on 12 Apr 2026 - 10:07

196

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Is the orthogonal polar factor the unique submersion satisfying an orthogonality relation?

Published on 10 Apr 2026 - 6:44

187

Views

Which matrices can be realized as second derivatives of orthogonal paths?

Published on 11 Apr 2026 - 21:38

List Question

Higher dimensional version of "a product of two reflections is a rotation"

Left cosets complex orthogonal group under real orthogonal group

Property of $Q$ such that $\frac{x^TQx}{\|x\|^2} = \text{const}, \ \ \ \forall x\in \mathbb{R}^n$

Can a linear isometry always be expressed in terms of an orthogonal matrix?

Show that there is an orthogonal matrix $O$ such that $OA_1=A_2O$.

Show that $L_A$ acts on by orthogonal transformation and in particular rotation.

Orthogonal transformation with additional constraints

Minimizing Frobenius norm of the difference between $A$ and $P^\top B P$

Basis of an Orthogonal Complement

If $A$ has orthonormal columns then $||Ax||^2_2 = ||x||^2_2$, why?

Is the orthogonal polar factor the unique retraction $\operatorname{GL}_n^+ \to \operatorname{SO}_n$?

Which matrices commute with $\operatorname{SO}_n$?

How can we decompose the identity matrix given a set of orthonormal vectors?

Is the orthogonal polar factor the unique submersion satisfying an orthogonality relation?

Which matrices can be realized as second derivatives of orthogonal paths?

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