MAPLE THROUGH EXAMPLES: MATRIX ALGEBRA

Maple is a scientific software that offers numerous possibilities for working in the field of matrix algebra. This book presents a wide variety of examples and solved exercises using Maple, covering the most common topics in matrix algebra. It delves into vector and matrix operators, variables, and functions, as well as operations with matrices, eigenvalues ​​and eigenvectors, matrix decomposition, similar matrices, diagonalization, and special matrices. Matrix applications are also shown in topics such as vector spaces, linear independence, bases, change of basis, vector geometry in 2 and 3 dimensions, linear transformations, quadratic forms, and the solution of equations and systems. Topics such as sequences, arrays, tables, lists, and sets are also covered. Furthermore, matrix applications to differentiability in several variables are addressed through Hessian matrices and their application in optimization. Matrix applications to vector differential calculus are also presented through Jacobian matrices, as well as matrix applications to operations research through linear programming and graph theory. The successive chapters present the topics to be covered, always illustrated through representative examples solved step by step using Maple. At the end of each chapter, exercises are provided to reinforce the concepts studied.