A note about some algebraic properties of matrix with progressions
Keywords:
Algebraic structures, groups and rings, teaching of algebraAbstract
This note introduces some matrices whose entries use arithmetic or geometric progressions for their formation. These
matrices appear in recreational mathematics (magic squares), cryptography and differential equations. Operations on
the set of these matrices are defined and it is proved that the sets of these matrices together with these operations have
group, ring and vector space structure.
References
[AR] Acosta-Humánez, P.; Ramı́rez-López, J. (2020). Differential equations with natural matrices coefficients. Journal of Physics: Conference Series. Volume 1514.012015. VI International Conference Days of Applied Mathematics (VI ICDAM) 16 October 2019, San José de Cúcuta, Colombia. pp. 1-5.
[An] Andrews W.S. (1917). Magic squares and cubes (2nd ed.). Open Court Publishing: https://archive.org/details/MagicSquaresCubesAndrewsEdited/page/n1/mode/2up, pp. 1-63.
[B] Bell, E. T. (1996). Historia de las Matemáticas. Fondo de Cultura Económica. México.
[F] Fraleigh, J.B. (1987). Álgebra Abstracta. Addison-Wesley Iberoamericana. Argentina.
[FCA] Francisco, J.; Carvajal, E.; Arreaza, T. (2014). Una clase de teorı́a de grupos usando progresiones aritméticas, geométricas y matrices cuadradas de orden impar. UNION. Revista Iberoamericana de Educación Matemática, 37, pp.57-70. España.
[H] Herstein, I. N. (1976). Álgebra moderna. Grupos, anillos, campos y teorı́a de Galois. Trillas, México.
[RG] Ramı́rez J, Gorrostola, J. (2012). Matrices Naturales. Revista Matua, 4, pp. 21-28.
[R] Rouse Ball W.W. (1905). Mathematical Recreations and Essays. MacMillan and Co. Fourth edition. Project Gutenberg : gutengerg.org/files/26839/26839-pdf.pdf , pp. 121-141.
[V] Voβ , Alexander W. (2006) Astronomı́a y matemáticas; en Nikolai Grube et al, Mayas. Una civilización milenaria, traducción de Mariona Gratacós i Grau, Marciano Villanueva, Lidia Álvarez Grifoll y Ambrosio Villanueva; pp.131-141 ; China, ed.Tandem Verlag GmbH.
[An] Andrews W.S. (1917). Magic squares and cubes (2nd ed.). Open Court Publishing: https://archive.org/details/MagicSquaresCubesAndrewsEdited/page/n1/mode/2up, pp. 1-63.
[B] Bell, E. T. (1996). Historia de las Matemáticas. Fondo de Cultura Económica. México.
[F] Fraleigh, J.B. (1987). Álgebra Abstracta. Addison-Wesley Iberoamericana. Argentina.
[FCA] Francisco, J.; Carvajal, E.; Arreaza, T. (2014). Una clase de teorı́a de grupos usando progresiones aritméticas, geométricas y matrices cuadradas de orden impar. UNION. Revista Iberoamericana de Educación Matemática, 37, pp.57-70. España.
[H] Herstein, I. N. (1976). Álgebra moderna. Grupos, anillos, campos y teorı́a de Galois. Trillas, México.
[RG] Ramı́rez J, Gorrostola, J. (2012). Matrices Naturales. Revista Matua, 4, pp. 21-28.
[R] Rouse Ball W.W. (1905). Mathematical Recreations and Essays. MacMillan and Co. Fourth edition. Project Gutenberg : gutengerg.org/files/26839/26839-pdf.pdf , pp. 121-141.
[V] Voβ , Alexander W. (2006) Astronomı́a y matemáticas; en Nikolai Grube et al, Mayas. Una civilización milenaria, traducción de Mariona Gratacós i Grau, Marciano Villanueva, Lidia Álvarez Grifoll y Ambrosio Villanueva; pp.131-141 ; China, ed.Tandem Verlag GmbH.
How to Cite
Carvajal Márquez, E. (2021). A note about some algebraic properties of matrix with progressions. Revista MATUA ISSN: 2389-7422, 8(1), 114–118. Retrieved from https://www.revistasuniatlanticoeduco.biteca.online/index.php/MATUA/article/view/2992
Downloads
Download data is not yet available.
Downloads
Published
2021-08-20
Issue
Section
Artículos
