- #1
krete
- 15
- 0
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
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