Abstract

In this paper I investigate properties of square complex matrices of the form A^k, where A is also a complex matrix, and k is a nonnegative integer. I look at several ways of representing A^k. 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 A^k. I also explain bounds on the norm of A^k, including some based on the element-based expression of T^k. Finally, I provide a detailed exposition of the most current form of the Kreiss Matrix Theorem.

Degree

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

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