MATHEMATICS: APPLIED LINEAR ALGEBRA & MATRIX ANALYSIS
CONTENTS LINEAR SYSTEMS OF EQUATIONS SOME EXAMPLES NOTATION AND A REVIEW OF NUMBERS GAUSSIAN ELIMINATION: BASIC IDEAS GAUSSIAN ELIMINATION: GENERAL PROCEDURE *COMPUTATIONAL NOTES AND PROJECTS MATRIX ALGEBRA MATRIX ADDITION AND SCALAR MULTIPLICATION MATRIX MULTIPLICATION APPLICATIONS OF MATRIX ARITHMETIC SPECIAL MATRICES AND TRANSPOSES MATRIX INVERSES BASIC PROPERTIES OF DETERMINANTS VECTOR SPACES DE?NITIONS AND BASIC CONCEPTS SUBSPACES LINEAR COMBINATIONS SUBSPACES ASSOCIATED WITH MATRICES AND OPERATORS BASES AND DIMENSION LINEAR SYSTEMS REVISITED GEOMETRICAL ASPECTS OF STANDARD SPACES STANDARD NORM AND INNER PRODUCT APPLICATIONS OF NORMS AND INNER PRODUCTS ORTHOGONAL AND UNITARY MATRICES *CHANGE OF BASIS AND LINEAR OPERATORS THE EIGENVALUE PROBLEM DE?NITIONS AND BASIC PROPERTIES SIMILARITY AND DIAGONALIZATION APPLICATIONS TO DISCRETE DYNAMICAL SYSTEMS ORTHOGONAL DIAGONALIZATION *SCHUR FORM AND APPLICATIONS *THE SINGULAR VALUE DECOMPOSITION GEOMETRICAL ASPECTS OF ABSTRACT SPACES NORMED SPACES INNER PRODUCT SPACES GRAM–SCHMIDT ALGORITHM *OPERATOR NORMS TABLE OF SYMBOLS SOLUTIONS TO SELECTED EXERCISES REFERENCES