Date Thesis Awarded
5-2011
Access Type
Honors Thesis -- Access Restricted On-Campus Only
Degree Name
Bachelors of Science (BS)
Department
Mathematics
Advisor
Charles R. Johnson
Committee Members
Joshua Erlich
Ilya Spitkovsky
Abstract
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.
Recommended Citation
Walch, Olivia J., "Critical Exponents: Old and New" (2011). Undergraduate Honors Theses. William & Mary. Paper 423.
https://scholarworks.wm.edu/honorstheses/423
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Comments
Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.