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

Fitri Aryani, Medyantiwi Rahmawita, Megawati and Sarbaini
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Fitri Aryani: Universitas Islam Negeri Sultam Syarif Kasim Riau, Indonesia
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

European Journal of Mathematics and Statistics, 2023, vol. 4, issue 4, 24-37

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.

Keywords: Mathematical induction; triangular matrix; matrix power; matrix trace (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:epw:ejmath:v:4:y:2023:i:4:id:14248

DOI: 10.24018/ejmath.2023.4.4.248

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