On the multiplicity of the eigenvalue


by krete
Tags: eigenvalue, multiplicity
krete
krete is offline
#1
Dec25-09, 02:54 AM
P: 15
On the multiplicity of the eigenvalue

Dear friends,
Might you tell me any hint on the multiplicity of the max eigenvalue, i.e., one, of the following matrix.

1 0 0 0 0
p21 0 p23 0 0
0 p32 0 p34 0
0 0 p43 0 p45
0 0 0 0 0

where, pij >0 and pi,i-1 + pi,i+1 = 1

It is clear that the above matrix has a max eigenvalue one. Moreover, my numeric simulation shows that the multiplicity of the max eigenvalue seems to be 1. However, I failed to prove this observation. Might you help me? Thanks a lot.

Merry Christmas
Phys.Org News Partner Science news on Phys.org
Lemurs match scent of a friend to sound of her voice
Repeated self-healing now possible in composite materials
'Heartbleed' fix may slow Web performance
kakaz
kakaz is offline
#2
Dec28-09, 05:21 AM
P: 17
Quote Quote by krete View Post
On the multiplicity of the eigenvalue

Dear friends,
Might you tell me any hint on the multiplicity of the max eigenvalue, i.e., one, of the following matrix.

1 0 0 0 0
p21 0 p23 0 0
0 p32 0 p34 0
0 0 p43 0 p45
0 0 0 0 0

where, pij >0 and pi,i-1 + pi,i+1 = 1

It is clear that the above matrix has a max eigenvalue one. Moreover, my numeric simulation shows that the multiplicity of the max eigenvalue seems to be 1. However, I failed to prove this observation. Might you help me? Thanks a lot.

Merry Christmas
Maxima gives me following eigenvalues for Your matrix: [latex] [[-\sqrt{p34*p43+p23*p32},\sqrt{p34*p43+p23*p32},0,1],[1,1,2,1]] [/latex] First vector are eigenvalues, second one - multiplicity.
krete
krete is offline
#3
Dec28-09, 06:10 AM
P: 15
Quote Quote by kakaz View Post
Maxima gives me following eigenvalues for Your matrix: [latex] [[-\sqrt{p34*p43+p23*p32},\sqrt{p34*p43+p23*p32},0,1],[1,1,2,1]] [/latex] First vector are eigenvalues, second one - multiplicity.
thank you very much for your kind help.


Register to reply

Related Discussions
multiplicity of a gas Introductory Physics Homework 1
eigenvalue - geometric multiplicity proof Calculus & Beyond Homework 1
eigenvalue with multiplicity k resulting in k orthogonal eigenvectors? Linear & Abstract Algebra 4
adjoint multiplicity Linear & Abstract Algebra 11
multiplicity in eigenvalues Calculus & Beyond Homework 1