- #1

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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