Characteristic Polynomials by Diagonal Expansion

This article describes the method of expansion by diagonal elements for the evaluation of the determinant of the sum of two square matrices, one of which is diagonal. This result is applied to the problem of obtaining the characteristic polynomial of a square matrix. For problems of interest in statistics, this technique is frequently much more direct than the usual approach of simplification (e.g., triangularization) by elementary row and column operations. Several examples are presented.