A characterization of -stable matrices

Abstract: In this paper we consider certain matrices A of size with exactly k ones in each row and each column where . We say that A is -isolated if there is a single zero entry in some submatrix of A. The submatrix need not be contiguous, i.e. formed from consecutive rows and consecutive columns of A. A is said to be -stable if A contains no -isolated zeros. Several examples are presented. We show that if A is -stable where then and we characterize the case of equality, when the matrix is not equivalent to a direct sum of matrices. [Copyright &y& Elsevier]