Bounding the Norm of Matrix Powers(2013)
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.
- matrix norm
Publication DateSummer July, 2013
DegreeMaster of Science
Field of studyMathematics
Citation InformationDaniel Ammon Dowler. "Bounding the Norm of Matrix Powers" (2013)
Available at: http://works.bepress.com/daniel-dowler/1/