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[SPECTRAL MAPPING THEOREM] Let \(A\) be a square matrix.

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[SPECTRAL MAPPING THEOREM] Let \(A\) be a square matrix.
a) If \(A(A-I)(A-2 I)=0\), show that the only possible eigenvalues of \(A\) are \(\lambda=0\), \(\lambda=1\), and \(\lambda=2\).
b) Let \(p\) any polynomial. Show that the eigenvalues of the matrix \(p(A)\) are precisely the numbers \(p\left(\lambda_{j}\right)\), where the \(\lambda_{j}\) are the eigenvalues of \(A\).
in Mathematics by Platinum (101k points) | 349 views

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