Question

$SO(N)$ generators to generate a basis for the space of $N\times N$ matrices

score 353 · Answer 1 · 2026-04-14 17:13:27

353

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$SO(N)$ generators to generate a basis for the space of $N\times N$ matrices

Published on 14 Apr 2026 - 17:13

score 270 · Answer 2 · 2026-04-15 11:02:52

270

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If $V \in \mathbb{R}^{n \times n}$ is an orthogonal matrix, and $V^T e=0$, ($e$ is the ones vector) then is it true $V_m^T e = 0\, \forall \, m<n$?

Published on 15 Apr 2026 - 11:02

score 906 · Answer 3 · 2026-04-15 21:37:53

906

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Do all orthogonal matrices satisfy both $Q^TQ = I$ and $QQ^T = I$?

Published on 15 Apr 2026 - 21:37

score 1.3k · Answer 4 · 2026-04-30 12:57:01

1.3k

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Orthogonal Block Matrix

Published on 30 Apr 2026 - 12:57

score 672 · Answer 5 · 2026-04-16 10:41:34

672

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All connected closed subgroups in $\rm{SO}(3)$

Published on 16 Apr 2026 - 10:41

score 351 · Answer 6 · 2026-04-15 23:38:27

351

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Classical Lie group quotient-ed by its maximal parabolic subgroup

Published on 15 Apr 2026 - 23:38

score 827 · Answer 7 · 2026-04-14 18:41:09

827

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$A^TA=B^TB$. Is $A=QB$ for some orthogonal $Q$?

Published on 14 Apr 2026 - 18:41

score 2.5k · Answer 8 · 2026-04-15 19:49:54

2.5k

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if $Q^TQ = I$, can we get $QQ^T=I$

Published on 15 Apr 2026 - 19:49

score 41 · Answer 9 · 2026-04-16 16:50:10

41

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If vector $y_1 = (1,2,3)$ and $y_2 = (4,5,6)$, how to calculate orthogonal projector $\prod\{y_1\}$ onto subspace spaned by the vectors $y_1,y_2$?

Published on 16 Apr 2026 - 16:50

score 47 · Answer 10 · 2026-04-13 11:27:31

47

Views

On a special decomposition of a $3\times 3$ matrix

Published on 13 Apr 2026 - 11:27

score 315 · Answer 11 · 2026-04-21 04:13:33

315

Views

Project an orthogonal matrix onto the Birkhoff Polytope

Published on 21 Apr 2026 - 4:13

score 185 · Answer 12 · 2026-04-15 22:02:12

185

Views

Prove matrix $A=(\cos\langle\alpha_i,\epsilon_j\rangle)_{n\times n}$ is orthogonal

Published on 15 Apr 2026 - 22:02

score 191 · Answer 13 · 2026-03-26 04:31:44

191

Views

Equivalence classes of orthogonal matrices

Published on 26 Mar 2026 - 4:31

score 203 · Answer 14 · 2026-04-10 21:54:22

203

Views

Linear-algebra first course problem about orthogonal matrices

Published on 10 Apr 2026 - 21:54

score 112 · Answer 15 · 2026-04-10 23:15:34

112

Views

Is the solution to $A-O(A)=\tilde \Sigma$ unique?

Published on 10 Apr 2026 - 23:15

List Question

$SO(N)$ generators to generate a basis for the space of $N\times N$ matrices

If $V \in \mathbb{R}^{n \times n}$ is an orthogonal matrix, and $V^T e=0$, ($e$ is the ones vector) then is it true $V_m^T e = 0\, \forall \, m<n$?

Do all orthogonal matrices satisfy both $Q^TQ = I$ and $QQ^T = I$?

Orthogonal Block Matrix

All connected closed subgroups in $\rm{SO}(3)$

Classical Lie group quotient-ed by its maximal parabolic subgroup

$A^TA=B^TB$. Is $A=QB$ for some orthogonal $Q$?

if $Q^TQ = I$, can we get $QQ^T=I$

If vector $y_1 = (1,2,3)$ and $y_2 = (4,5,6)$, how to calculate orthogonal projector $\prod\{y_1\}$ onto subspace spaned by the vectors $y_1,y_2$?

On a special decomposition of a $3\times 3$ matrix

Project an orthogonal matrix onto the Birkhoff Polytope

Prove matrix $A=(\cos\langle\alpha_i,\epsilon_j\rangle)_{n\times n}$ is orthogonal

Equivalence classes of orthogonal matrices

Linear-algebra first course problem about orthogonal matrices

Is the solution to $A-O(A)=\tilde \Sigma$ unique?

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