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Critical Exponents: Old and New

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Author: Walch, Olivia J.
Advisor: Johnson, Charles R.
Committee Members: Erlich, Joshua; Spitkovsky, Ilya
Issued Date: 5/14/2011
URI: http://hdl.handle.net/10288/13734
Description: 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.
Degree: Bachelors of Science in Mathematics

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