On the multiplicity of the eigenvalue

  1. 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
     
  2. jcsd
  3. Maxima gives me following eigenvalues for Your matrix: [itex] [[-\sqrt{p34*p43+p23*p32},\sqrt{p34*p43+p23*p32},0,1],[1,1,2,1]] [/itex] First vector are eigenvalues, second one - multiplicity.
     
  4. thank you very much for your kind help.
     
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