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Eigenvalues of 2 matrices are equal

  1. Dec 19, 2013 #1
    Hi all,

    I have two matrices
    A=0 0 1 0
    0 0 0 1
    a b a b
    c d c d
    and B=0 0 0 0
    0 0 0 0
    0 0 a b
    0 0 c d
    I need to prove that two eigenvalues of A and two eigenvalues of B are equal. I tried to take the determinant of A-λI and B-λI and solve them but the result is not complete, the result that I got is
    if e,f,g,h are eigenvalues of A and i,j,k,l are eigenvalues of B then
    e+f+g+h=a+d;
    i+j=a+d, k=l=0;
    e*f*g*h=i*j;
    efg+fgh+efh+egh=-2ij

    Can anyone get me the complete result that is two eigenvalues of A and B are equal?

    Thanks
     
  2. jcsd
  3. Dec 19, 2013 #2

    AlephZero

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