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Math Help - eigenvectors/eigenvalues

  1. #1
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    eigenvectors/eigenvalues

    A ∈ Rn*n and X is an eigenvector of A with eigenvalue . P is a nonsingular matrix.

    Show directly from the de nition that P^1 X is an eigenvector for P^1 AP with eigenvalue

    im struggling with even starting this? any suggestions would be appreciated
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  2. #2
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    we know that Ax = βx.

    so what is P^-1AP(P^-1x)? (hint: P^-1AP(P^-1x) = P^-1(A(P(P^-1x))), and P(P^-1(x)) = x).
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  3. #3
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    thanks for the help ill attempt now
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