Sign Patterns for Eigenmatrices of Nonnegative Matrices
نویسنده
چکیده
For a square (0, 1,−1) sign pattern matrix S, denote the qualitative class of S by Q(S). In this paper, we investigate the relationship between sign patterns and matrices that diagonalise an irreducible nonnegative matrix. We explicitly describe the sign patterns S such that every matrix in Q(S) diagonalises some irreducible nonnegative matrix. Further, we characterise the sign patterns S such that some member of Q(S) diagonalises an irreducible nonnegative matrix. Finally, we provide necessary and sufficient conditions for a multiset of real numbers to be realised as the spectrum of an irreducible nonnegative matrix M that is diagonalised by a matrix in the qualitative class of some SNS sign pattern.
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