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.

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Identifier

honors_theses/145