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

Kobal, Damjan (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: analogy, zero, numbers, matrices, polynomials
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: Str. 951-963
• Številčenje: Vol. 35, no. 9/10
• PID: 20.500.12556/RUL-179895
• UDK: 512:37.091.3
• ISSN pri članku: 1051-1970
• DOI: 10.1080/10511970.2024.2352362
• COBISS.SI-ID: 227129603
• Datum objave v RUL: 26.02.2026

Gradivo je del revije

• Naslov: PRIMUS : problems, resources, and issues in mathematics undergraduate studies
• Skrajšan naslov: PRIMUS
• Založnik: Taylor & Francis
• ISSN: 1051-1970
• COBISS.SI-ID: 514635033

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.