Sign patterns of nonnegative normal matrices

Sign Patterns for Eigenmatrices of Nonnegative Matrices

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 ...

Eventually Nonnegative Matrices and their Sign Patterns

A matrix A ∈ Rn×n is eventually nonnegative (respectively, eventually positive) if there exists a positive integer k0 such that for all k ≥ k0, A ≥ 0 (respectively, A > 0). Here inequalities are entrywise and all matrices are real and square. An eigenvalue of A is dominant if its magnitude is equal to the spectral radius of A. A matrix A has the strong Perron-Frobenius property if A has a uniqu...

On nonnegative sign equivalent and sign similar factorizations of matrices

Patterns of alternating sign matrices

Article history: Received 14 April 2011 Accepted 1 March 2012 Available online xxxx Submitted by N. Shaked-Monderer In admiration, to Avi Berman, Moshe Goldberg, and Raphi Loewy AMS classification: 05B20 05C22 05C50 15B36

Ela on Nonnegative Sign Equivalent and Sign Similar Factorizations of Matrices∗

Dedicated to Hans Schneider on the occasion of his eightieth birthday Abstract. It is shown that every real n×n matrix is a product of at most two nonnegative sign equivalent matrices, and every real n × n matrix, n ≥ 2, is a product of at most three nonnegative sign similar matrices. Finally, it is proved that every real n×n matrix is a product of totally positive sign equivalent matrices. How...