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Eventually Positive Matrices and Tree Sign Patterns
Waugh, Madellyne
Waugh, Madellyne
Abstract
A n-by-n matrix A is said to be eventually positive if there is a power k such that $A^k$ is entrywise positive, and all subsequent powers are also entrywise positive. Here we provide an expression for the smallest such exponent of a 2-by-2 eventually positive matrix in terms of its entries; we also show that if the graph of an eventually positive matrix is a tree, then the positive part of that matrix must be primitive.
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2019-12-01
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Mathematics