Properties of Matrices and Systems of Linear Equations

Abstract

This document is not intended to be a course on all numerical methods, much less a course on matrix. The idea is to give at the beginning of this document the essentials on matrix, then the methods for solving systems of linear algebraic equations. Certainly, in the literature many methods exist, we find direct methods and iterative methods. Only direct methods are treated to enable the resolution of systems of linear algebraic equations. The most used direct methods are direct elimination, Cramer's rule, Gauss elimination, Gauss-Jordan elimination, matrix inversion and matrix factorization. At the beginning, this course intended for the third year of the degree aimed to teach students programming techniques, including the FORTRAN and MATLAB programming languages. Noticing huge gaps among students in matrix operations and numerical methods, the content of this course has been improved and adapted for our students, to make this course available to them, this course was produced mainly from “Numerical Methods for Engineers and Scientists” by Joe D. Hoffman. This course is devoted only to the matrix operations part and numerical methods for solving systems of linear equations.