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Abstract:
Let M stand for a matrix in M(n,C), the algebra of n x n matrices with
complex entries and let F(x) be a polynomial in C[x] the algebra of
polynomials with complex coefficients. This talk deals with the
question "Are there any matrices S in M(n,C) satisfying the equation
F(S) = M?" A complete description and an algorithm to construct all
such S satisfying the additional condition that S is in C[M], the
algebra of polynomials in M with complex coefficients is provided. As
a corollary, all S in C[M] satisfying the equation Sm = M, where m is
a positive integer, are determined.
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