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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Dowler, Daniel Ammon, "Bounding the Norm of Matrix Powers" (2013). All Theses and Dissertations. 3692.
Matrix Powers, Matrix Norm Bounds, Matrix Power Bounds, Kreiss Matrix Theorem, Schur Decomposition, Schur Form