A Polynomial in A of the Diagonalizable and Nilpotent Parts of A

Title: A Polynomial in A of the Diagonalizable and Nilpotent Parts of A
Author: Kathryn Wilson
Faculty Sponsor: Scott Beaver; Gavin Keulks
Date: 6/1/2017
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.
Type: Text; Honors Thesis
Department: Honors Program
Language: eng
Rights: Western Oregon University Library has determined, as of 06/01/2023, this item is in copyright, which is held by the author. Users may use the item in accordance with copyright limitations and exceptions, including fair use. For other uses, please ask permission from the author.; http://rightsstatements.org/vocab/InC/1.0/
Identifier: honors_theses/145