# On the multiplicity of the eigenvalue

by krete
Tags: eigenvalue, multiplicity
 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
P: 17
 Quote by krete 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: $[[-\sqrt{p34*p43+p23*p32},\sqrt{p34*p43+p23*p32},0,1],[1,1,2,1]]$ First vector are eigenvalues, second one - multiplicity.
P: 15
 Quote by kakaz Maxima gives me following eigenvalues for Your matrix: $[[-\sqrt{p34*p43+p23*p32},\sqrt{p34*p43+p23*p32},0,1],[1,1,2,1]]$ First vector are eigenvalues, second one - multiplicity.
thank you very much for your kind help.

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