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Thesis
Bounding the Norm of Matrix Powers
(2013)
  • Daniel Ammon Dowler, Brigham Young University
Abstract
In this paper I investigate properties of square complex matrices of the form Ak , where A is also a complex matrix, and k is a nonnegative integer. I look at several ways of representing Ak . In particular, I present an identity expressing the k th power of the Schur form T of A in terms of the elements of T, which can be used together with the Schur decomposition to provide an expression of Ak . I also explain bounds on the norm of Ak , including some based on the element-based expression of Tk . Finally, I provide a detailed exposition of the most current form of the Kreiss Matrix Theorem.
Keywords
  • Kreiss,
  • matrix norm
Disciplines
Publication Date
Summer July, 2013
Degree
Master of Science
Field of study
Mathematics
Department
Mathematics
Advisor
Jeffrey Humpherys
Citation Information
Daniel Ammon Dowler. "Bounding the Norm of Matrix Powers" (2013)
Available at: http://works.bepress.com/daniel-dowler/1/