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Matrix zeros of polynomials

Published online by Cambridge University Press:  02 March 2020

Damjan Kobal
Damjan Kobal*
Affiliation:
Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia e-mail: damjan.kobal@fmf.uni-lj.si
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Extract

The concepts of polynomials and matrices essentially expand and enhance the elementary arithmetic of numbers. Once introduced, polynomials and matrices open up new interesting mathematical challenges which extend to new fields of mathematical explorations within university mathematics. We present an aspect of a rather elementary exploration of polynomials and matrices, which offers a new perspective and an interesting matrix analogue to the concept of a zero of a polynomial. The discussion offers an opportunity for better comprehension of the fundamental concepts of polynomials and matrices. As an application we are led to the meaningful questions of linear algebra and to an easy proof of the otherwise advanced and abstract Cayley-Hamilton theorem.

Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 559 , March 2020 , pp. 27 - 35
Copyright
© Mathematical Association 2020

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