Question

If $\lambda$ is an eigenvalue of an orthogonal matrix $C$, prove $\frac{1}{\lambda}$ is an eigenvalue of $C^T$

score 2.4k · Answer 1 · 2026-02-23 18:33:06

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If $\lambda$ is an eigenvalue of an orthogonal matrix $C$, prove $\frac{1}{\lambda}$ is an eigenvalue of $C^T$

Published on 23 Feb 2026 - 18:33

score 2.1k · Answer 2 · 2015-11-23 15:53:39

2.1k

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Find a real orthogonal matrix of order $3$ , other than +- I_3 ,having all integer elements.

Published on 23 Nov 2015 - 15:53

score 1.1k · Answer 3 · 2016-01-06 21:40:17

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Parametrization of $3 \times 3$ real orthogonal matrices

Published on 06 Jan 2016 - 21:40

score 3.5k · Answer 4 · 2026-02-26 12:37:08

3.5k

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Show that $O(n)$, the set of orthogonal $n \times n$ matrices, is not connected

Published on 26 Feb 2026 - 12:37

score 832 · Answer 5 · 2016-03-26 22:50:38

832

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Given matrices $A,B$, minimize $\|UAV^T - B\|_F$ over orthogonal matrices $U, V$

Published on 26 Mar 2016 - 22:50

score 1.9k · Answer 6 · 2026-03-25 22:15:52

1.9k

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Is an orthogonal matrix necessarily a permutation matrix?

Published on 25 Mar 2026 - 22:15

score 210 · Answer 7 · 2016-05-24 15:08:28

210

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Orthogonal matrix $Q$ such that $\forall x\leq 0$, $Qx\geq 0$

Published on 24 May 2016 - 15:08

score 2.3k · Answer 8 · 2016-06-03 10:54:56

2.3k

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Show that $x$ and $Q x$ are equidistant

Published on 03 Jun 2016 - 10:54

score 100 · Answer 9 · 2016-06-04 09:48:42

100

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Prove that if $A^t = A^{-1}$ then different rows of $A$ are orthogonal to each other

Published on 04 Jun 2016 - 9:48

score 1.3k · Answer 10 · 2016-06-07 10:18:58

1.3k

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Orthogonal matrix of symmetric matrix (eigenvectors)

Published on 07 Jun 2016 - 10:18

score 2.4k · Answer 11 · 2016-06-08 10:16:48

2.4k

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Show any orthogonal matrix is similar to an almost diagonal matrix, with either $\pm 1$ or a 2D rotation on the diagonal

Published on 08 Jun 2016 - 10:16

score 99 · Answer 12 · 2016-06-18 13:01:57

99

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If a matrix is such that its inverse is equal to its transpose, does it belong to the special orthogonal group

Published on 18 Jun 2016 - 13:01

score 11.4k · Answer 13 · 2016-06-19 16:55:20

11.4k

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For an orthogonal matrix $Q$, why does $QQ^T = I$?

Published on 19 Jun 2016 - 16:55

score 3.7k · Answer 14 · 2016-06-19 19:51:27

3.7k

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What exactly does a rotation preserve?

Published on 19 Jun 2016 - 19:51

score 2.1k · Answer 15 · 2016-06-20 12:17:58

2.1k

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Prove the orthogonal matrix with determinant 1 is a rotation

Published on 20 Jun 2016 - 12:17

List Question

If $\lambda$ is an eigenvalue of an orthogonal matrix $C$, prove $\frac{1}{\lambda}$ is an eigenvalue of $C^T$

Find a real orthogonal matrix of order $3$ , other than +- I_3 ,having all integer elements.

Parametrization of $3 \times 3$ real orthogonal matrices

Show that $O(n)$, the set of orthogonal $n \times n$ matrices, is not connected

Given matrices $A,B$, minimize $\|UAV^T - B\|_F$ over orthogonal matrices $U, V$

Is an orthogonal matrix necessarily a permutation matrix?

Orthogonal matrix $Q$ such that $\forall x\leq 0$, $Qx\geq 0$

Show that $x$ and $Q x$ are equidistant

Prove that if $A^t = A^{-1}$ then different rows of $A$ are orthogonal to each other

Orthogonal matrix of symmetric matrix (eigenvectors)

Show any orthogonal matrix is similar to an almost diagonal matrix, with either $\pm 1$ or a 2D rotation on the diagonal

If a matrix is such that its inverse is equal to its transpose, does it belong to the special orthogonal group

For an orthogonal matrix $Q$, why does $QQ^T = I$?

What exactly does a rotation preserve?

Prove the orthogonal matrix with determinant 1 is a rotation

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