Date Thesis Awarded
Honors Thesis -- Open Access
Bachelors of Science (BS)
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.
Waugh, Madellyne, "Eventually Positive Matrices and Tree Sign Patterns" (2019). Undergraduate Honors Theses. William & Mary. Paper 1470.