Matrix Roots of Nonnegative and Eventually Nonnegative Matrices
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Eventually nonnegative matrices are real matrices whose powers become and remain nonnegative. As such, eventually nonnegative matrices are, a fortiori, matrix roots of nonnegative matrices, which motivates us to study the matrix roots of nonnegative matrices. Using classical matrix function theory and Perron-Frobenius theory, we characterize, classify, and describe in terms of the complex and real Jordan canonical form the pth-roots of nonnegative and eventually nonnegative matrices.