AN EXPLICIT FORM OF POWERS OF A 2 × 2 MATRIX USING A RECURSIVE SEQUENCE

Abstract

The purpose of this paper is to derive powers An using a system of recursive sequences for a given 2×2 matrix A. Introducing a recursive sequence we have a quadratic equation. Solutions to this quadratic equation are related with eigenvalues of A. By solving this quadratic equation we can easily obtain an explicit form of An. Our method holds when A is defined not only on the real field but also on the complex field.

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