实二阶方阵正整数方幂迹的计算  

Trace calculation of positive integer power of real 2×2 matrices

作　　者：麦麦提明·阿不都克力木 Mamantimin·Adbikirim(School of Mathematics and Statistics,Kashi University,Kashi 844006,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844006

出　　处：《高师理科学刊》2020年第3期19-22,共4页Journal of Science of Teachers＇College and University

摘　　要：讨论实二阶方阵正整数方幂迹的计算问题,得到了计算实二阶方阵A正整数方幂迹的一个新公式,此公式只涉及矩阵A的迹trA、行列式detA和n(正整数)次乘法.特别地,当trA或detA为零时,得到了计算trA^n的一些特例.The calculation of trace of any positive integer power of 2×2 real matrix is discussed,a new formula for calculating the trace of any positive integer power of 2×2 real matrix A is obtained,this formula only involves the trace of A(trA)and determinant of A(detA),and n times multiplication of the matrix,where n is positive integer.Especially,when trAor detAis zero,some special cases of calculating trA^n are obtained.

关 键 词：迹 行列式 矩阵乘法 

分 类 号：O151.21[理学—数学]