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4
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1
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Singular values of random uniform matrix
Suppose $X \in \mathbb{R}^{N \times M}$ with elements sampled i.i.d. from $\mathcal{U}(-\sigma, \sigma)$.
I would like to find the marginal distribution of the unordered singular values of $X$.
The ...
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2
votes
1
answer
834
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Jacobian of changing of variables to singular value decomposition
It is well known that changing variables from a symmetric matrix to its eigenvalue decomposition involves a Jacobian which is just the Vandermonde determinant of the eigenvalues.
Now suppose I have a ...
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3
votes
1
answer
3k
views
Singular value decomposition of random rectangular matrices
Let $A$ be a $m\times n$ real matrix, whose entries are independent, identically distributed random variables, following standard normal distributions (mean zero and unit variance).
What is the ...
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