Trace of Positive Integer Power of Real 2 × 2 Matrices

Abstract

The purpose of this paper is to discuss the theorems for the trace of any positive integer power of 2 × 2 real matrix. We obtain a new formula to compute trace of any positive integer power of 2 × 2 real matrix A, in the terms of Trace of A (TrA) and Determinant of A (DetA), which are based on definition of trace of matrix and multiplication of the matrixn times, where n is positive integer and this formula gives some corollary for TrAn when TrA or DetA are zero.