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Math Help - show any square matrix in C has at least one eigenvalue

  1. #1
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    show any square matrix in C has at least one eigenvalue

    show any square matrix in C has at least one eigenvalue
    Last edited by mr fantastic; January 17th 2009 at 06:49 PM. Reason: Replaced "As title" with the title to assist quoting of the post in replies
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  2. #2
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    Quote Originally Posted by silversand View Post
    show any square matrix in C has at least one eigenvalue
    An  n \times n matrix will always yield a characteristic equation which is a polynomial of order n.

    By the fundamental theorem of algebra, any non-constant single variable polynomial with complex coefficients has at least 1 complex root. Eigenvalues are roots of the characteristic equation.
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