List questions from orthogonal-matrices

Published on 25 Mar 2026 - 20:34

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Dimensions of Orthogonal Group Representations

Published on 19 Mar 2021 - 3:19

80

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On state-transition matrix and fundamental theorem of local theory of curves

Published on 21 Mar 2021 - 16:36

49

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If $f: (-1,1)→M_n(\mathbb R)$ be a $C^1$ map such that $f(0)=I$ and $f(t)\in O(n)$ ,show that $Df(0)$ exists and is a skew-symmetric matrix

Published on 21 Mar 2021 - 18:22

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What happens to the trace if you multiply with orthogonal matrices

Published on 22 Mar 2021 - 15:04

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Cardinal of the Special Orthogonal Group $SO_n\left(\mathbb{Z}/2^n\mathbb{Z}\right)$

Published on 23 Mar 2021 - 20:09

144

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$SU(2)$ and the $3$-sphere, with $SO(2)$ a longitude

Published on 26 Mar 2026 - 22:13

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Definition of orthogonal projection of a matrix

Published on 28 Mar 2026 - 12:14

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Show that $O_2(\mathbb{R})$ contains only rotational and reflective symmetries.

Published on 30 Mar 2021 - 7:35

128

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Show that $(A-I)^{-1}(A+I)$ is orthogonal if $A$ is skew-symmetric

Published on 26 Mar 2026 - 17:53

68

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How can I obtain $B = B^{T}$ if $A = 2 B − I$ is an isometry and $B^2 = B$?

Published on 01 Apr 2021 - 18:49

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$QR$ decomposition of block matrix

Published on 28 Mar 2026 - 23:10

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Is there a natural way to "project" an arbitrary matrix to an orthogonal matrix?

Published on 25 Mar 2026 - 3:07

243

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If a square matrix's column vectors and row vectors all have norm 1, then is the matrix orthonormal?

Published on 26 Apr 2021 - 23:15

120

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Diagonalization of a real symmetric matrix

Published on 29 Apr 2021 - 18:24

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Orthogonal transformations and matrices having similar eigenvalues

Dimensions of Orthogonal Group Representations

On state-transition matrix and fundamental theorem of local theory of curves

If $f: (-1,1)→M_n(\mathbb R)$ be a $C^1$ map such that $f(0)=I$ and $f(t)\in O(n)$ ,show that $Df(0)$ exists and is a skew-symmetric matrix

What happens to the trace if you multiply with orthogonal matrices

Cardinal of the Special Orthogonal Group $SO_n\left(\mathbb{Z}/2^n\mathbb{Z}\right)$

$SU(2)$ and the $3$-sphere, with $SO(2)$ a longitude

Definition of orthogonal projection of a matrix

Show that $O_2(\mathbb{R})$ contains only rotational and reflective symmetries.

Show that $(A-I)^{-1}(A+I)$ is orthogonal if $A$ is skew-symmetric

How can I obtain $B = B^{T}$ if $A = 2 B − I$ is an isometry and $B^2 = B$?

$QR$ decomposition of block matrix

Is there a natural way to "project" an arbitrary matrix to an orthogonal matrix?

If a square matrix's column vectors and row vectors all have norm 1, then is the matrix orthonormal?

Diagonalization of a real symmetric matrix

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