0
$\begingroup$

the singular value decomposition of an $m\times n$ random Gaussian matrix ${\displaystyle \mathbf {M} }$ is a factorization of the form ${\displaystyle \mathbf {U\Sigma V^\ast} }$, ${\displaystyle \mathbf {\Sigma } }$ is an ${\displaystyle m\times n}$ rectangular diagonal matrix with non-negative ordred real numbers on the diagonal, my question is:

What is the distribution of the singular values of $\Sigma $?

can I say that the singular value corresponds to the absolute value of Gaussian variable?

$\endgroup$
2
$\begingroup$

With fixed ratio $\lambda=m/n$ the Marchenko-Pastur distribution gives the asymptotic distribution of singular values for a Gaussian rectangular matrix.

The extreme singular values limiting distribution in particular is given by the Tracy-Widom distribution.

Also, the singular values do not have limiting distribution corresponding to the absolute value of a Gaussian distribution.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.