Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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AN EXPLICIT FORM OF POWERS OF A $2{\times}2$ MATRIX USING A RECURSIVE SEQUENCE

  • Published : 2012.02.15
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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

References

  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.

Cited by

  1. THE RELATIONSHIP BETWEEN THE POWERS OF AN INVERTIBLE MATRIX AND THOSE OF ITS INVERSE vol.25, pp.4, 2012, https://doi.org/10.14403/jcms.2012.25.4.609