Hi, Ravi,
Thank you, but I did not get it!
I tried hard by specifying the vector of probabilities, but it always gives zeros and all integers as eigenvalues. 
The eigenvalues need to be not just integers and they should satisfy order requirement.
Any more suggestions?
Regards,
-Chee



From: Ravi Varadhan 
Sent: Friday, April 15, 2011 8:14 AM
To: Chee Chen ; r-help@r-project.org 
Subject: RE: [R] How to generate a correlation matrix with restrictions on its eigenvalues


Generate random numbers from a multinomial.

?rmultinom
# The following will generate n multinomial vectors each of size m
rmultinom(n, size=m, prob=m^(-1/8))  # you need to specify probabilities appropriately

Ravi.
________________________________________
From: r-help-bounces@r-project.org [r-help-bounces@r-project.org] On Behalf
Sent: Thursday, April 14, 2011 11:55 PM
To: r-help@r-project.org
Subject: [R] How to generate a correlation matrix with restrictions on its      eigenvalues

Dear All,
I would like to generate m positive real numbers c_i, I=1,...,m, such that
(1) c_1 + c_2 + ... + c_m=m,
(1) after being ordered  into c_1 >= c_2 >= .... >=c_m>0,  we have that c_m is of the same order of m^(-1/8), when m is sufficiently large.
Thanks,
-Chee



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