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 kth 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.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2013-07-05

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd6434

Keywords

Matrix Powers, Matrix Norm Bounds, Matrix Power Bounds, Kreiss Matrix Theorem, Schur Decomposition, Schur Form

Included in

Mathematics Commons

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