AN EXPLICIT FORM OF POWERS OF A $2{\times}2$ MATRIX USING A RECURSIVE SEQUENCE
Daniel Kim, Sangwoo Ryoo, Taesoo Kim, Hasik Sunwoo · Journal of the Chungcheng Mathematical Society · 2012
The purpose of this paper is to derive powers $A^{n}$ using a system of recursive sequences for a given $2{\times}2$ 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 $A^{n}$ . Our method holds when A is defined not only on the real field but also on the complex field.