[R] Matrix question
apjaworski@mmm.com
apjaworski at mmm.com
Wed Apr 14 02:50:42 CEST 2004
Gideon,
Eigenvectors are normalized to unit length. The first eigenvector
calculated by R is equal (ignoring the signs of course) to your stable
distribution vector divided by its length.
Andy
__________________________________
Andy Jaworski
518-1-01
Process Laboratory
3M Corporate Research Laboratory
-----
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Tel: (651) 733-6092
Fax: (651) 736-3122
|---------+-------------------------------->
| | GIDEON WASSERBERG |
| | <wasserberg at wisc.edu>|
| | Sent by: |
| | r-help-bounces at stat.m|
| | ath.ethz.ch |
| | |
| | |
| | 04/13/2004 18:28 |
|---------+-------------------------------->
>-----------------------------------------------------------------------------------------------------------------------------|
| |
| To: "R-help at lists.R-project.org" <R-help at stat.math.ethz.ch> |
| cc: |
| Subject: [R] Matrix question |
>-----------------------------------------------------------------------------------------------------------------------------|
Dear Friends
I am doing a simple matrix analysis to calculate the eigenvalue,
eigenvector using R for the below matrix, and comparing the result to those
obtained from a projection (using excel)
THE MATRIX:
> c
[,1] [,2] [,3]
[1,] 0.0 2.0 2
[2,] 0.8 0.0 0
[3,] 0.0 0.8 0
The dominant eigenvalue comes out comparable to that calculated
numerically, but the eigenvectors do not( see below)!
EIGENVALUES (calculated by R):
> eigen(c)
$values
[1] 1.5564082+0.000000i -0.7782041+0.465623i -0.7782041-0.465623i
EIGENVALUE numerically calculated: 1.556408145
EIGENVECTORS (calculated by R):
$vectors
[,1] [,2] [,3]
[1,] -0.8658084+0i 0.6476861+0.0000000i 0.6476861+0.0000000i
[2,] -0.4450290+0i -0.4902997-0.2933611i -0.4902997+0.2933611i
[3,] -0.2287467+0i 0.2382837+0.4441499i 0.2382837-0.4441499i
Stable age distribution (calculated numerically):
0.562365145
0.289057934
0.148576921
My questions are:
1. Both eigenvalue and eigenvectors are associated with some imaginary
value (i). How should I relate to that information? 2. More importantly, a.
I presume the 1st eigenvector collumn [,1] should correspond to the
dominant eigenvalue. How come then that it comes out different from the one
calculated numerically? Is there some conversion I should do?
Many thanks
Gideon
Gideon Wasserberg (Ph.D.)
Wildlife research unit,
Department of wildlife ecology,
University of Wisconsin
218 Russell labs, 1630 Linden dr.,
Madison, Wisconsin 53706, USA.
Tel.:608 265 2130, Fax: 608 262 6099
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