##plugins.themes.bootstrap3.article.main##

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.

References

  1. Brezinski C, Fika P, Mitrouli M. Estimations of the Trace of Powers of Positive Self-Adjoint Operators by Extrapolation of the Moments. Electronic Transactions on Numerical Analysis. 2012 May 7; 39:144–155.
     Google Scholar
  2. Pahade J, Jha M. Trace of Positive Integer Power of Real 2 × 2 Matrices. Advances in Linear Algebra & Matrix Theory. 2015 Desember; 5 (4): 150–155.
     Google Scholar
  3. Aryani F, Solihin M. Trace Matriks Real Berpangkat Bilangan Bula Negatif, Jurnal Sains Matematika dan Statistika. 2017 Juli; 3 (2): 16–23.
     Google Scholar
  4. Aryani F, Yulianis. Trace Matriks Berbentuk Khusus 2×2 Berpangkat Bilangan Bulat Negatif. Jurnal Sains Matematika dan Statistika. 2018 Juli; 4 (2): 105–113.
     Google Scholar
  5. Aryani F, Cenia PB, Muda Y, Zukrianto Trace Matriks Simetris Berbentuk Khusus Orde 3 Berpangkat Bilangan Bulat. Prosiding Nasional pada Seminar Nasional Teknologi Informasi, Komunikasi dan Industri (SNTIKI); 2021 Nov 18; (13): 300–310.
     Google Scholar
  6. Aryani F, Harnita, Muda Y, Zukrianto. Trace Matriks Simetris Berbentuk Khusus 4 x 4 Berpangkat Bilangan Bulat. Prosiding Nasional pada Seminar Nasional Teknologi Informasi, Komunikasi dan Industri (SNTIKI); 2021 Nov 18; (13): 311–321.
     Google Scholar
  7. Aryani F, Alfinov SP, Marzuki CC, Rahma AN, Trace Matriks Simetris Berbentuk Khusus 5 x 5 Berpangkat Bilangan Bulat. (SNTIKI); 2021 Nov18; (13): 322–333.
     Google Scholar
  8. Rahmawati, Putri NA, Aryani F, Rahma AN. Trace Matriks Toeplitz Simetris Bentuk Khusus 3×3 Berpangkat Bilangan Bulat Positif. Jurnal Sains Matematika dan Statistika. 2019 Juli; 5 (2): 61–70.
     Google Scholar
  9. Aryani F, Andesta R, Marzuki CC. Trace Matriks Berbentuk Khusus 3×3 Berpangkat Bilangan Bulat Positif. Jurnal Sains Matematika dan Statistika. 2020 Januari; 6 (1): 40–9.
     Google Scholar
  10. Aryani F, Taslim R. Trace Matrix 3 x 3 Berpangkat Bilangan Bulat. Jurnal Sains Matematika dan Statistika. 2021 Januari; 7 (1): 1–9.
     Google Scholar
  11. Marjono. Linear Algebra. Malang UB Press; 2012.
     Google Scholar
  12. Gentle JE. Matrix algebra, vol. 10. Springer; 2007.
     Google Scholar
  13. Kariadinata R. Algebra of Elementary Matrices. Bandung Pustaka Setia; 2013.
     Google Scholar
  14. Larson R. Elementary Linear Algebra. 7th ed. Boston Cengage Learning; 2013.
     Google Scholar
  15. Rosen KH. Discrete Mathematics and Its Applications. New York Mc Graw Hill; 2007.
     Google Scholar
  16. Munir R. Discrete Mathematics. Bandung Informatics ITB; 2005.
     Google Scholar
  17. Rifa'I R. Basic Matrix Algebra. Yogyakarta Budi Utama; 2016.
     Google Scholar
  18. Banerjee S, Roy A. Linear Algebra and Matrix Analysis for Statistics. Crc Press Boca Raton; 2014.
     Google Scholar
  19. Anton H, Rorres C. Elementary Linear Algebra. United States of America Wiley; 2013.
     Google Scholar