The Formula of the Trace of Triangle n×n Matrix to the Power of Positive Integer

Abstract

This study determined the general form of the trace of the triangular matrices n × n with the power of positive integer. Before obtaining the general form of the trace of triangular matrices (upper triangle and lower triangle) n × n with the power positive integer, first obtain the general form of the triangular matrices n × n with power positive integer. Obtaining the general form of the triangular matrices n × n with the power positive integer is carried out by determining of the triangular matrices from power two to power eight. It is further suspected that the general form of a triangular matrices n × n with the power of a positive integer and prove it using mathematical induction. Finally, a triangular matrices trace n × n with the power of a positive integer is obtained with direct proof based on the general form of the matrices has been obtained. Given the application trace of the triangle matrices n × n with power positive integer by an example.