List questions from orthogonal-matrices

Published on 16 May 2020 - 2:40

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Operators on an Euclidean space

Published on 25 Mar 2026 - 17:36

52

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A problem about operators on an Euclidean space

Published on 25 Mar 2026 - 17:36

79

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Question about Orthonormal Bases

Published on 18 May 2020 - 22:30

229

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How to show: Matrix $H_v = I - 2vv^{\top}$ with $||v|| =1$ to the reflection on hyperplane $v^{\bot}$ is symetrical and orthogonal and $det H_v = -1$?

Published on 26 Mar 2026 - 8:02

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Opposite determinant in Autonne-Takagi factorization

Published on 25 Mar 2026 - 14:21

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Does $A^TA=I$ imply $AA^T=I$?

Published on 29 May 2020 - 10:54

259

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Best approximation of a vector $x=\begin{bmatrix}2&2&0&0\end{bmatrix}^\tau$ by the vectors in $M^\perp$, where $b\in M$ is given

Published on 30 May 2020 - 0:17

1.4k

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determinant of an orthogonal matrix

Published on 30 May 2020 - 2:42

99

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If $V$ is right-orthogonal, does it hold $\langle AV,BV\rangle_F=\langle A,B\rangle_F$?

Published on 01 Jun 2020 - 10:06

1k

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Othorgonal matrices and full rank

Published on 01 Jun 2020 - 14:00

1k

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Solving system of linear equations using orthogonal matrix

Published on 03 Jun 2020 - 14:15

791

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unitary operator explanation

Published on 25 Mar 2026 - 16:06

550

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Are orthogonal operators always isomorphisms?

Published on 25 Mar 2026 - 19:25

148

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Isomorphism between $SO_2\tilde{\times}\mathbb{Z}_2$ and $O_2$

Published on 05 Jun 2020 - 10:30

List Question

For rotation matrices in SO(3), solutions of AB = BA given A (or B)

Operators on an Euclidean space

A problem about operators on an Euclidean space

Question about Orthonormal Bases

How to show: Matrix $H_v = I - 2vv^{\top}$ with $||v|| =1$ to the reflection on hyperplane $v^{\bot}$ is symetrical and orthogonal and $det H_v = -1$?

Opposite determinant in Autonne-Takagi factorization

Does $A^TA=I$ imply $AA^T=I$?

Best approximation of a vector $x=\begin{bmatrix}2&2&0&0\end{bmatrix}^\tau$ by the vectors in $M^\perp$, where $b\in M$ is given

determinant of an orthogonal matrix

If $V$ is right-orthogonal, does it hold $\langle AV,BV\rangle_F=\langle A,B\rangle_F$?

Othorgonal matrices and full rank

Solving system of linear equations using orthogonal matrix

unitary operator explanation

Are orthogonal operators always isomorphisms?

Isomorphism between $SO_2\tilde{\times}\mathbb{Z}_2$ and $O_2$

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