From: Dave Rusin <rusin@math.niu.edu>
Subject: Re: distribution of eigenvalue
Date: Fri, 18 Jun 1999 13:44:18 -0500 (CDT)
Newsgroups: sci.math.research
To: esmaila@mcmail.cis.McMaster.CA
Keywords: random matrices

In article <375CBEC7.836E1B31@mcmail.mcmaster.ca> you write:
>Hi
>I am trying to transform the distribution of the elements of a matrix
>into its eigenvalues.  For example let matrix X be a 2x2 matrix with
>real values:
>X=[a b
>      c d]
>and let each element of this matrix be normally distribution with a
>covariance matrix given by a 4x4 matrix (note: a,b,c, and d are not
>independent).  What is the p.d.f. of the (eig(X))? and is it possible to
>derive the same distribution for the case when X is any real nxn matrix?
>
>    I have been looking at Mathematical Statistic books, with limited
>success.  Any help would be appreciated.

I don't know the answer to your question. There is a book which seems
appropriate; here is the listing from Math Reviews.

[deletia --djr]

dave


   98b:60114 60H25 (15-02 15A52 62H99)
   Girko, Vyacheslav L.(UKR-KIEV-AS)
   Theory of linear algebraic equations with random coefficients. 
   Allerton Press, Inc., New York, 1996. xxiv+320 pp. $120.00. ISBN
   0-89864-078-4

   This monograph is written with the aim of giving a systematic and
   self-contained presentation of results on systems of linear algebraic
   equations with random coefficients. The author is a well-known
   specialist in multivariate statistical analysis, spectral theory of
   random matrices, and stochastic equations theory. This book can be
   useful for those who work with applications of stochastic methods in
   physics, multivariate statistical analysis, linear programming and
   experiment planning.
     
                        Reviewed by Alexei Khorunzhy

   Copyright American Mathematical Society 1999