AN EXPLICIT FORM OF POWERS OF A 2 x2 MATRIX USING A RECURSIVE SEQUENCE

• 발행기관: 충청수학회
• 저자명: Daniel Kim Sangwoo Ryoo Taesoo Kim Hasik Sunwoo
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 25, No. 1, 19~25쪽, 전체 7쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2012.02.28

영문 초록

The purpose of this paper is to derive powers An using a system of recursive sequences for a given 2£2 matrix A. Introduc-ing a recursive sequence we have a quadratic equation. Solutions to this quadratic equation are related with eigenvalues of A. By solv-ing this quadratic equation we can easily obtain an explicit form of An. Our method holds when A is de¯ned not only on the real ¯eld but also on the complex ¯eld.

목차

1. Introduction