List questions from orthogonal-matrices

Published on 07 May 2026 - 18:35

71

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How to prove that $\langle P,A^2 \rangle \le 0 $ for every positive $P$ and skew-symmetric $A$?

Published on 12 Apr 2026 - 12:19

45

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Does there exist any non-trivial linear relation on the components of elements of $O(2,1)$?

Published on 14 Apr 2026 - 20:43

94

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When does $P\text{SO}P^{-1} \subseteq \text{SO}$?

Published on 16 Apr 2026 - 7:50

1.6k

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Lie algebra: intuition of "Lie Algebra is tangent space of corresponding Lie Group"?

Published on 11 May 2026 - 3:17

235

Views

Reducing the quadratic form

Published on 11 Apr 2026 - 7:21

18

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Why is the maximum value of an orthonormal dictionary of size $N \times N$ less than that of another having size $M \times M$, where M>N?

Published on 15 Apr 2026 - 22:58

49

Views

Proof based on orthogonal matrix

Published on 14 Apr 2026 - 8:51

1k

Views

Orthogonal matrix multiplied by diagonal matrix multiplied by transpose of the orthogonal matrix

Published on 16 Apr 2026 - 14:12

63

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Minimum singular value of sum of rotations

Published on 14 Apr 2026 - 12:39

11.4k

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Does 3x4 matrix have an Inverse? Why?

Published on 08 Apr 2026 - 22:47

161

Views

Householder matrices for thin QR updating

Published on 10 Apr 2026 - 1:53

60

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Matrices in $\operatorname{O}(n) \setminus \operatorname{SO}(n)$

Published on 13 Apr 2026 - 1:37

2.5k

Views

Haar measure from axis-angle representation of $SO(3)$

Published on 10 May 2026 - 15:09

86

Views

Question about a proof that the eigenvalues of an $n \times n$ orthogonal matrix are $\pm 1$

Published on 14 Apr 2026 - 8:11

List Question

The orbit space GL(n,R)/O(n)

How to prove that $\langle P,A^2 \rangle \le 0 $ for every positive $P$ and skew-symmetric $A$?

Does there exist any non-trivial linear relation on the components of elements of $O(2,1)$?

When does $P\text{SO}P^{-1} \subseteq \text{SO}$?

Lie algebra: intuition of "Lie Algebra is tangent space of corresponding Lie Group"?

Reducing the quadratic form

Why is the maximum value of an orthonormal dictionary of size $N \times N$ less than that of another having size $M \times M$, where M>N?

Proof based on orthogonal matrix

Orthogonal matrix multiplied by diagonal matrix multiplied by transpose of the orthogonal matrix

Minimum singular value of sum of rotations

Does 3x4 matrix have an Inverse? Why?

Householder matrices for thin QR updating

Matrices in $\operatorname{O}(n) \setminus \operatorname{SO}(n)$

Haar measure from axis-angle representation of $SO(3)$

Question about a proof that the eigenvalues of an $n \times n$ orthogonal matrix are $\pm 1$

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