Honors Senior Theses/Projects

Date of Award

6-1-2017

Faculty Advisor

Scott Beaver

Abstract

Any square matrix A can be decomposed into a sum of the diagonal (DA) and nilpotent (NA) parts as A = DA + NA. The components DA and NA commute with each other and with A. For many matrices A; B, if B commutes with A, then B is a polynomial in A; this holds for DA and NA. Following a Herbert A. Medina preprint, this paper shows how to construct the polynomials p(A) = NA and q(A) = DA. Further, the Jordan canonical form J is a conjugate QAQ^-1 of A; this paper demonstrates that the conjugation relating J and A also relates NA and NJ and DA and DJ, respectively.

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