List questions from orthogonal-matrices

Published on 30 Jan 2022 - 19:49

102

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How to show that there is a non-zero $v \in \mathbb{R}^n$ for any $A \in O(n)$ s.t $Av=\pm v$ whenever $n$ is odd.

Published on 05 Feb 2022 - 17:04

1.3k

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Number of independent elements of an orthogonal matrix

Published on 08 Feb 2022 - 12:04

510

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When $A \in SO(3)$, $A$ is always a rotation.

Published on 31 Mar 2026 - 12:43

37

Views

Quadratic forms and orthogonal basis

Published on 12 Feb 2022 - 22:13

181

Views

If a linear map sends orthonormal basis on orthonotmal basis then it is an isometry?

Published on 31 Mar 2026 - 12:44

135

Views

QR decomposition and a change of basis

Published on 17 Feb 2022 - 18:48

116

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Commutativity of Multiplying Semi-orthogonal Matrix with Symmetric Matrix

Published on 23 Feb 2022 - 8:34

177

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Is there a name for this 'splitting' of an orthogonal structure into unitary and symplectic structures?

Published on 24 Feb 2026 - 2:18

67

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Questions regarding a proof of "classification of the finite subgroups of $SO(3)$".

Published on 01 Mar 2022 - 6:19

104

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Curve with a prescribed Frenet frame

Published on 25 Mar 2026 - 17:45

75

Views

Question regarding the Three orbit case of classification of finite subgroups of $SO(3)$. (Tetrahedral Group)

Published on 03 Mar 2022 - 8:29

159

Views

The conjugation action $\mathbb{H}^*\times \mathbb{H} \rightarrow \mathbb{H}$ restricted to unit-quaternions yields an orthogonal representation

Published on 07 Mar 2022 - 11:43

181

Views

Orthogonal Matrix with respect to different inner products

Published on 18 Mar 2022 - 19:15

60

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Matrix representation of a reflection

Published on 22 Mar 2022 - 10:55

List Question

Decomposition of a matrix with orthogonal columns

How to show that there is a non-zero $v \in \mathbb{R}^n$ for any $A \in O(n)$ s.t $Av=\pm v$ whenever $n$ is odd.

Number of independent elements of an orthogonal matrix

When $A \in SO(3)$, $A$ is always a rotation.

Quadratic forms and orthogonal basis

If a linear map sends orthonormal basis on orthonotmal basis then it is an isometry?

QR decomposition and a change of basis

Commutativity of Multiplying Semi-orthogonal Matrix with Symmetric Matrix

Is there a name for this 'splitting' of an orthogonal structure into unitary and symplectic structures?

Questions regarding a proof of "classification of the finite subgroups of $SO(3)$".

Curve with a prescribed Frenet frame

Question regarding the Three orbit case of classification of finite subgroups of $SO(3)$. (Tetrahedral Group)

The conjugation action $\mathbb{H}^*\times \mathbb{H} \rightarrow \mathbb{H}$ restricted to unit-quaternions yields an orthogonal representation

Orthogonal Matrix with respect to different inner products

Matrix representation of a reflection

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