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Results tagged with orthogonal-groups
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user 11260
5
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Probability distribution of vectors obtained from Gram-Schmidt process on i.i.d. Gaussian ve...
The orthogonalization requires $N\leq K$. For $N=K$ the resulting $N\times N$ unitary matrix is distributed according to the Haar measure, see On asymptotics of large Haar distributed unitary matrices …
- 188k
12
votes
Computing Haar measure of matrices sampled from SO(n)
Indeed, the distribution function of the eigenphases of a random matrix in $\operatorname{SO}(n)$ has a peak at 0 and at $\pm\pi$. It only becomes uniform for large $n$. The joint distribution functio …
- 188k