Re: Mean singular values

> If I have a M times N matrix A which only contains complex random
> values, all selected from an Gaussian distribution with a given mean
> and variance, then are there any expressions available who give the
> mean value of the largest/smallest singular values of A ?
>
> It is easy to numerically compute the mean of largest/smallest
> singular value in for example Matlab but I would suspect an
> analytical answer may be available in the literature. Random
> Matrix theory ? Any references would be appreciated. Thanks!

You may find the answer in Alan Edelman's thesis (which you can find on
his home page, http://www-math.mit.edu/~edelman/).

See also:

Eigenvalues and condition numbers of random matrices, by A. Edelman. SIAM
Journal on Matrix Analysis and Applications 9 (1988), 543--560.

where you can find pdf's for the smallest and largest singular values
and simple formulas for the expected values if m,n->oo.


Daniel