Primitive zero-symmetric sign pattern matrices with the maximum base
نویسندگان
چکیده
منابع مشابه
Primitive Zero-Symmetric Sign Pattern Matrices with Zero Diagonal Attaining the Maximum Base
A sign pattern matrix or sign pattern A is a matrix whose entries are from the set {1,−1, 0}. Notice that for a square sign pattern matrixA, in the computation of the signs of the entries of the power A, an ambiguous sign may arise when a positive sign is added to a negative sign. So a new symbol # was introduced in 1 to denote such an ambiguous sign. The powers of a square sign pattern have be...
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In this note we consider completions of n×n symmetric (0,−1)-matrices to symmetric alternating sign matrices by replacing certain 0s with +1s. In particular, we prove that any n×n symmetric (0,−1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with +1s can be completed to a symmetric alternating sign matrix. Similarly, any n × n symmetric (0,+1)-matrix that can ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.03.003