Polynomial Equations over Matices.

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Hellenbrand, Kaitlyn

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If we are given an n-th degree polynomial over the complex numbers, we know that it has exactly n solutions. However, this is not true for an n-th degree polynomial over matrices. The difference in the two cases is that multiplication of matices is not commutative (AB does not equal BA) and not all matrices are invertible. The question then becomes: how many solutions can exist?

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University of Wisconsin--Eau Claire Office of Research and Sponsored Programs.

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