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Solutions of Polynomials over Matrices

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Author(s)
Hellenbrand, Kaitlyn
Advisor(s)
Duffy, Colleen M.
Date
Apr 2010
Subject(s)
Matrices; Polynomials; Posters
Series
USGZE AS589
Abstract
If we are given an Nth degree polynomial over the complex numbers, we know that it has exactly n solutions. However, this is not true for an Nth degree polynomial over matrices. The reason lies in the many differences between matrices, which are a ring, and complex numbers, which are a field. The question then becomes: How many solutions exist? Researchers have developed a geometric approach to solving this problem, which shows the maximum number of diagonalizable solutions for an Nth degree polynomial over k x k matrices. This approach also leads to results that demonstrate which numbers of diagonalizable solutions are possible.
Description
Color poster with text, equations, and diagrams.
Sponsor(s)
University of Wisconsin--Eau Claire Office of Research and Sponsored Programs
Permanent link
http://digital.library.wisc.edu/1793/47086 
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