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Eigen values of transpose

  1. Jun 22, 2011 #1
    A is a square matrix over F field

    if k is the eigen value of A



    prove that k is eigen value of A^t too

    and has the same eigen vectors

    ??



    eigen vectors are the solution space P(A)

    is found by solving (A-kI)x=0

    dim P(A)=dim n -dim (ro(a))

    rho(a)=rho(a^t)

    |A|=|A^t|



    these are the laws i maneged to come up with to solve it



    ??
     
    Last edited: Jun 22, 2011
  2. jcsd
  3. Jun 22, 2011 #2
    We know that the eigenvalues of a matrix A are all the scalars k that satisfy the characteristic equation det( A - k In ) = 0.

    We also know that det( A ) = det( A^t ) for any square matrix A.

    Can we use these facts to complete a proof?
     
  4. Jun 22, 2011 #3
    ok i prooved that the eigen values are the same
    hw to prove that the eigen vectors are the same to for every eigen value
     
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