Analogy and generalization as a driving force of learning mathematics - the case of a matrix analog of a zero of a polynomial

Kobal, Damjan (author)

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 analog 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.

• Language: English
• Keywords: analogy, zero, numbers, matrices, polynomials
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 951-963
• Numbering: Vol. 35, no. 9/10
• PID: 20.500.12556/RUL-179895
• UDC: 512:37.091.3
• ISSN on article: 1051-1970
• DOI: 10.1080/10511970.2024.2352362
• COBISS.SI-ID: 227129603
• Publication date in RUL: 26.02.2026

Record is a part of a journal

• Title: PRIMUS : problems, resources, and issues in mathematics undergraduate studies
• Shortened title: PRIMUS
• Publisher: Taylor & Francis
• ISSN: 1051-1970
• COBISS.SI-ID: 514635033

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.