List questions from orthogonal-matrices

Published on 25 Mar 2026 - 19:00

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Sub-determinants of an orthogonal matrix

Published on 20 Mar 2012 - 20:27

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Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal

Published on 10 May 2012 - 22:35

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In which cases is the inverse of a matrix equal to its transpose?

Published on 10 Jun 2012 - 23:08

978

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Intersection of the sets of generalized doubly stochastic matrices and of orthogonal matrices

Published on 16 Jun 2012 - 17:16

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A unitary matrix taking a real matrix to another real matrix, is it an orthogonal matrix?

Published on 26 Mar 2026 - 12:07

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Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?

Published on 01 Oct 2012 - 21:45

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If $A$ is skew-symmetric, then $I-A$ is invertible and $Q = (I-A)^{-1}(I+A)$ is orthogonal

Published on 26 Mar 2026 - 14:35

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Show that the cyclic shift operator is unitary

Published on 25 Mar 2026 - 13:59

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Orthogonal matrix with eigenvalues $\in \mathbb{R}$ is symmetric

Published on 05 Feb 2013 - 19:12

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Difference between orthogonal and orthonormal matrices

Published on 26 Mar 2026 - 12:04

1.3k

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Nonnegative orthogonal matrices

Published on 25 Mar 2026 - 5:59

6.9k

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Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$

Published on 30 Mar 2013 - 14:21

76

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Given orthogonal matrix $P$, is $P \circ P$ invertible?

Published on 26 Mar 2026 - 12:52

97

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Singular values of matrices which preserve the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} \le 1$

Published on 02 Aug 2020 - 7:36

List Question

Completing a unitary matrix given a column

Sub-determinants of an orthogonal matrix

Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal

In which cases is the inverse of a matrix equal to its transpose?

Intersection of the sets of generalized doubly stochastic matrices and of orthogonal matrices

A unitary matrix taking a real matrix to another real matrix, is it an orthogonal matrix?

Is $O_n$ isomorphic to $SO_n \times \{\pm I\}$?

If $A$ is skew-symmetric, then $I-A$ is invertible and $Q = (I-A)^{-1}(I+A)$ is orthogonal

Show that the cyclic shift operator is unitary

Orthogonal matrix with eigenvalues $\in \mathbb{R}$ is symmetric

Difference between orthogonal and orthonormal matrices

Nonnegative orthogonal matrices

Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$

Given orthogonal matrix $P$, is $P \circ P$ invertible?

Singular values of matrices which preserve the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} \le 1$

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