ALGEBRAIC PROPERTIES OF NATURAL MATRICES
Abstract
Natural matrices, introduced by the first author more than twenty years ago, are very important in several areas such as computational security, cryptography, dynamical systems, differential equations, biology and physics, among others researches that are currently in progress. The main aim of this paper is to present new algebraic results in natural matrices which were included in the first part of the master thesis in applied mathematics of the first author, supervised by the second author. These results are original and correspond to the master thesis of the first author, supervised by the second author. We rewrite some classical results of abstract and linear algebra through Natural Matrices. Finally, we establish beautiful and useful relationships between Natural Matrices and Magic Squares, which are very important in recreational mathematics
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[2] Ramírez J, Gorrostola J 2014 Matrices Naturales, X Encuentro Internacional de Matemáticas EIMAT Universidad del Atlántico - Barranquilla.
[3] Ramírez J, Gorrostola, J 2015 Suma Sucesiva, Revista MATUA 2 48-56.
[4] Ramírez J, Gorrostola J 2015 Proyecciones de las matrices naturales en el estudio de la teoría del pegar y reversar y en la fundamentación matemática de la raíz digital aplicada en programación, XI Encuentro Internacional de Matemáticas EIMAT Universidad del Atlántico - Barranquilla.
[5] Ramírez J, Gorrostola, J 2015 Matrices Naturales, Revista MATUA, 4 21-28.
[6] Acosta-Humánez P 2003 La Operación Pegamiento y el Cuadrado de Números Naturales, Revista Civilizar, Universidad Sergio Arboleda - Bogotá.
[7] Acosta-Humánez P, Molano P, Rodríguez A 2015 Algunas Observaciones Sobre Pegar y Reversar en Números Naturales, Revista MATUA 2 65-90.
[8] Hernández P 2009 Sobre la raíz digital de los números primos, Revista Digital Matemáticas, Educación e Internet, 10 1-5.
[9] Shafarevich, I R, Remizov, A O 2012 Linear Algebra and Geometry, Springer, Germany
[10] Ayres F 1989 Algebra Moderna, Serie Schaum McGraw-Hill, México.
[11] Acosta-Humánez P, Chuquen A 2016 Pasting and Reversing Approach to Matrix Theory, Journal of Algebra, Number Theory and Applications 38 535-559.
[12] Acosta-Humánez P, Chuquen A, Rodríguez A 2015 Pasting and Reversing Operations over some Vector Spaces, Boletín de Matemáticas 20 65-90.
[13] Acosta-Humánez P, Martínez O 2015 A Simple Permutations with Order 4n+ 2 by Means of Pasting and Reversing, Qualitative Theory of Dynamical Systems 15 1811-210.
[14] Acosta-Humanez P, Jiménez G. 2019 Some tastings in Morales-Ramis theory, J. Phys.: Conf. Ser. 1414 012011
[15] Block, S 2009 Before Sudoku: The World of Magic Squares. Oxford University Press, United Kingdom
McCranie, J 1988 Magic Squares of All Orders, Mathematics Teacher 81 674-678.
