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Math Help - Characteristic Value and Vector

  1. #1
    Junior Member
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    Characteristic Value and Vector

    If A is nonsingular, show that the characteristic values of A^-1 are the reciprocals of A, and the A and A^-1 have the same characteristic vectors.

    I need help getting started on this. Any help would be greatly appreciated. Thanks,

    Jim
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  2. #2
    Newbie
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    May 2008
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    Fix an eigenvalue \lambda of A and let v be an eigenvector w.r.t. the eigenvalue, write down  Av=\lambda v. Since A is invertible, \lambda is nonzero and you can multiply both sides of the equation by the inverse of A.
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