List questions from orthogonal-matrices

Published on 25 Mar 2026 - 14:21

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Step in PCA proof - invariance of trace operator and orthogonality

Published on 25 Mar 2026 - 3:20

183

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Sum of two rotations of the same matrix

Published on 22 Mar 2026 - 6:34

468

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Is the Euclidean distance from $\text{SO}(n)$ approximately convex?

Published on 25 Mar 2026 - 3:02

288

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Show that $|A-I|=0$

Published on 21 Mar 2026 - 17:58

144

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Orthogonal group representation induces an isometry on $L^p$ spaces

Published on 20 Mar 2026 - 13:33

49

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Searching for orthogonal matrices with some property

Published on 22 Mar 2026 - 12:52

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How to generate orthogonal matrices?

Published on 22 Mar 2026 - 1:57

304

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Prove that if $\Vert{Qx}\Vert = \Vert{x}\Vert$ then $Q^{-1} = Q^{t}$

Published on 25 Mar 2026 - 6:12

224

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Find orthogonal complement and its basis

Published on 22 Mar 2026 - 10:15

103

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Show that $\mathbf{M}^T\mathbf{M}^{-1}\left(\mathbf{M}^{-1}\right)^T\mathbf{M}=I$ where $\mathbf{M}= I - \mathbf{A}$ and $\mathbf{A}^T = - \mathbf{A}$

Published on 25 Mar 2026 - 9:16

866

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Number of equations in orthogonal matrix?

Published on 22 Mar 2026 - 10:35

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If an orthogonal matrix has determinant -1 then it has -1 as an eigenvalue

Published on 12 May 2018 - 22:05

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If $\lambda$ is an eigen value of an orthogonal matrix $A$, then show that $\frac{1}{\lambda}$ is also an eigen value of $A$

Published on 13 May 2018 - 5:52

117

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Eigenvectors of a vectorized tranpose matrix

Published on 22 Mar 2026 - 15:52

List Question

Direct sum of two subspace

Step in PCA proof - invariance of trace operator and orthogonality

Sum of two rotations of the same matrix

Is the Euclidean distance from $\text{SO}(n)$ approximately convex?

Show that $|A-I|=0$

Orthogonal group representation induces an isometry on $L^p$ spaces

Searching for orthogonal matrices with some property

How to generate orthogonal matrices?

Prove that if $\Vert{Qx}\Vert = \Vert{x}\Vert$ then $Q^{-1} = Q^{t}$

Find orthogonal complement and its basis

Show that $\mathbf{M}^T\mathbf{M}^{-1}\left(\mathbf{M}^{-1}\right)^T\mathbf{M}=I$ where $\mathbf{M}= I - \mathbf{A}$ and $\mathbf{A}^T = - \mathbf{A}$

Number of equations in orthogonal matrix?

If an orthogonal matrix has determinant -1 then it has -1 as an eigenvalue

If $\lambda$ is an eigen value of an orthogonal matrix $A$, then show that $\frac{1}{\lambda}$ is also an eigen value of $A$

Eigenvectors of a vectorized tranpose matrix

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