Ravi Varadhan wrote:
Hi,
Given a positive integer N, and a real number \lambda such that 0 < \lambda
< 1, I would like to generate an N by N stochastic matrix (a matrix with
all the rows summing to 1), such that it has the second largest eigenvalue
equal to \lambda (Note: the dominant eigenvalu
A further idea:
Consider the triangular square matrices of the form with decreasing
eigenvalues on the diagonal:
1 0 0 0 0 0
.3 .7 0 0 0 0
.4 .2 .4 0 0 0
.2 .4 .2 .2 0 0
.1 .3 .4 .2 .1 0
.2 .2 .2 .2 .1 .1
This would have the specified eigenvalue compo
--
> ---
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvarad...@jhmi.edu
On Oct 15, 2009, at 6:24 PM, Ravi Varadhan wrote:
Hi,
Given a positive integer N, and a real number \lambda such that 0 <
\lambda
< 1, I would like to generate an N by N stochastic matrix (a matrix
with
all the rows summing to 1), such that it has the second largest
eigenvalue
equal to
625
Email: rvarad...@jhmi.edu
Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h
tml
-Original Message-
From: Albyn Jones [mailto:jo...@reed.edu]
Sent: Thursday, October 15, 2009 6:56 PM
To: Ravi Varadhan
Cc: r-help@r-project.org
Subject: Re: [R] Generating a s
I just tried the following shot in the dark:
generate an N by N stochastic matrix, M. I used
M = matrix(runif(9),nrow=3)
M = M/apply(M,1,sum)
e=eigen(M)
e$values[2]= .7 (pick your favorite lambda, you may need to fiddle
with the others to guarantee this is second largest
Hi,
Given a positive integer N, and a real number \lambda such that 0 < \lambda
< 1, I would like to generate an N by N stochastic matrix (a matrix with
all the rows summing to 1), such that it has the second largest eigenvalue
equal to \lambda (Note: the dominant eigenvalue of a stochastic ma
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