A Diagrammatic Approach for the Coefficients of the Characteristic Polynomial

TL;DR

This paper introduces a novel diagrammatic method using circle graphs to efficiently compute the coefficients of a matrix's characteristic polynomial, offering a visual and potentially more intuitive approach.

Contribution

The paper presents a new diagrammatic technique employing circle graphs to calculate characteristic polynomial coefficients, differing from traditional algebraic methods.

Findings

Circle graph representations accurately compute polynomial coefficients.

The diagrammatic approach simplifies the calculation process.

Potential for visual intuition in linear algebra computations.

Abstract

In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ a diagrammatic approach to determine the coefficients of the characteristic polynomial.