[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2012.25.1.019

AN EXPLICIT FORM OF POWERS OF A $2{\times}2$ MATRIX USING A RECURSIVE SEQUENCE

Kim, Daniel (Chungbuk Science High School)
Ryoo, Sangwoo (Chungbuk Science High School)
Kim, Taesoo (Chungbuk Science High School)
SunWoo, Hasik (Department of Mathematics Konkuk University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.25, no.1, 2012 , pp. 19-25 More about this Journal

Abstract

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.

Keywords

powers of a matrix; a recursive sequence; diagonalisation;

Citations & Related Records

Reference

1	R. Bronson, Matrix Methods An Introduction 2nd Ed., Academic Press, Inc., New York, 1991.
2	S. K. Ko, An Introduction to Complex Analysis (in Korean), Kyungmoon Publishers, Seoul, 2007.
3	S. R. Searle, Matrix Algebra Useful for Statistics, Wiley-Interscience, New York, 2006.

KSCI

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

AN EXPLICIT FORM OF POWERS OF A $2{\times}2$ MATRIX USING A RECURSIVE SEQUENCE