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MATHEMATICA is a scientific computing software widely used in the experimental sciences. This book develops MATHEMATICA applications in the field of linear algebra. The following topics are covered: VARIABLES AND FUNCTIONS 1.1 VARIABLES 1.2 FUNCTIONS DEFINITION 1.3 RECURSIVE FUNCTIONS 1.4 PIECEWISE FUNCTIONS 1.5 OPERATIONS WITH FUNCTIONS 1.6 DATA TYPES USED IN THE DEFINITION OF THE FUNCTIONS NUMBERS, OPERATIONS AND MOST COMMON FUNCTIONS. NUMBERING SYSTEMS 2.1 OPERATIONS ARITHMETIC 2.2 FUNCTIONS PREDEFINED OF INTEGER ARGUMENT 2.3 NUMBERING SYSTEMS 2.4 RATIONAL NUMBERS 2.5 IRRATIONAL NUMBERS 2.6 COMPLEX NUMBERS. MORE COMMON FUNCTIONS 2.7 ROUNDING AND APPROACH FUNCTIONS 2.8 COMMON CONSTANT USED IN MATHEMATICA 2.9 RANDOM NUMBERS 2.10 EL PACKAGE OF NUMBER THEORY ALGEBRAIC EXPRESSIONS, POLYNOMIALS, AND INTERPOLATION 3.1 FUNCTIONS COMMON ALGEBRAIC OPERATIONS 3.2 POLYNOMIALS 3.3 OPERATIONS ALGEBRAIC WITH POLYNOMIALS 3.4 POLYNOMIAL INTERPOLATION 3.5 EL PACKAGE NUMERICALMATH 'APPROXIMATIONS' 3.6 POLYNOMIAL ADJUSTMENT EQUATIONS AND SYSTEMS 4.1 RESOLUTION OF EQUATIONS 4.2 SPECIAL COMMANDS TO SOLVE EQUATIONS 4.3 NUMERICAL METHODS FOR RESOLUTION OF EQUATIONS 4.4 SYSTEMS OF EQUATIONS MATRIX ALGEBRA 5.1 VECTORS 5.2 OPERATIONS WITH VECTORS 5.3 MATRICES 5.4 OPERATIONS WITH MATRICES 5.5 SPECIAL OPERATIONS WITH MATRICES 5.6 MATRIX DECOMPOSITION 5.7 RANGE OF A MATRIX VECTOR SPACES AND LINEAR APPLICATIONS. LINEAR SYSTEMS 5.8 LINEAR INDEPENDENCE. BASES. CHANGE OF BASIS 5.9 LINEAR APPLICATIONS 5.10 QUADRATIC FORMS 5.11 SYSTEMS OF LINEAR EQUATIONS 5.12 ROUCHE -FROBENIUS THEOREM 5.13 HOMOGENEOUS SYSTEMS The topics are illustrated with many examples and exercises solved.