Research Article

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

Fitri Aryani
Universitas Islam Negeri Sultam Syarif Kasim Riau, Indonesia
* Corresponding author
Medyantiwi Rahmawita
Universitas Islam Negeri Sultam Syarif Kasim Riau, Indonesia
Megawati
Universitas Islam Negeri Sultam Syarif Kasim Riau, Indonesia.
Sarbaini
Universitas Islam Negeri Sultam Syarif Kasim Riau, Indonesia
DOI icon 10.24018/ejmath.2023.4.4.248

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Submitted 2023-05-08
Published 2023-07-28

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Article Main Content

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.

Keywords: Mathematical induction triangular matrix matrix power matrix trace

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