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Math Help - [SOLVED] Eigenvalues

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    [SOLVED] Eigenvalues

    Let A be a real 2x2 matrix.
    If A has two distinct eigenvalues, then {A^2 } has two distinct eigenvalues.

    False, does anyone know a counterexample or relevant theorem of definition?
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    Quote Originally Posted by dwsmith View Post
    Let A be a real 2x2 matrix.
    If A has two distinct eigenvalues, then {A^2 } has two distinct eigenvalues.

    False, does anyone know a counterexample or relevant theorem of definition?
    If \lambda is an eigenvalue of A then \lambda^2 is an eigenvalue of A^2

    Now you just need a 2 by 2 matrix eigenvalue \pm 1.
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