Date Thesis Awarded
Bachelors of Science (BS)
Charles R. Johnson
Let P be a class of matrices, and let A be an m-by-n matrix in the class. The critical exponent of P, if it exists, with respect to some notion of continuous powering is the lowest power g(P) such that for any matrix B in P, B^t is in P for all t > g(P). This paper considers two questions for several classes P (including doubly nonnegative and totally positive): 1) does a critical exponent g(P) exist? and 2) if so, what is it? For those where no exact result has been determined, lower and upper bounds are provided.
Walch, Olivia J., "Critical Exponents: Old and New" (2011). Undergraduate Honors Theses. Paper 423.
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