Linear Algebra

Cover Copyright Contents Preface Preface to the Second Edition A Note to Students List of Symbols Matrices 1.1INTRODUCTION 1.2BASIC CONCEPTS 1.3 MATRIX OPERATIONS AND THEIR PROPERTIES 1.4 INVERTIBLE MATRICES 1.5 TRANSPOSE OF A MATRIX 1.6 PARTITION OF MATRICES; BLOCK MULTIPLICATION 1.7 GROUPS AND FIELDS Systems of LinearEquations 2.1 INTRODUCTION 2.2 GAUSSIAN ELIMINATION 2.3 ELEMENTARY ROW OPERATIONS 2.4 ROW REDUCTION 2.5 INVERTIBLE MATRICES AGAIN 2.6 LU FACTORIZATION 2.7 DETERMINANT Vector Spaces 3.1 INTRODUCTION 3.2 BASIC CONCEPTS 3.3 LINEAR INDEPENDENCE 3.4 BASIS AND DIMENSION 3.5 SUBSPACES AGAIN 3.6 RANK OF A MATRIX 3.7 ORTHOGONALITY IN Rn 3.8 BASES OF SUBSPACES 3.9 QUOTIENT SPACE Linear Mapsand Matrices 4.1 INTRODUCTION 4.2 BASIC CONCEPTS 4.3 ALGEBRA OF LINEAR MAPS 4.4 ISOMORPHISM 4.5 MATRICES OF LINEAR MAPS Linear Operators 5.1 INTRODUCTION 5.2 POLYNOMIALS OVER FIELDS 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES 5.4 MINIMAL POLYNOMIAL 5.5 INVARIANT SUBSPACES 5.6 SOME BASIC RESULTS 5.7 REAL QUADRATIC FORMS Canonical Forms 6.1 INTRODUCTION 6.2 PRIMARY DECOMPOSITION THEOREM 6.3 JORDAN FORMS Bilinear Forms 7.1 INTRODUCTION 7.2 BASIC CONCEPTS 7.3 LINEAR FUNCTIONALS AND DUAL SPACE 7.4 SYMMETRIC BILINEAR FORMS 7.5 GROUPS PRESERVING BILINEAR FORMS Inner Product Spaces 8.1 INTRODUCTION 8.2 HERMITIAN FORMS 8.3 INNER PRODUCT SPACE 8.4 GRAM–SCHMIDT ORTHOGONALIZATION PROCESS 8.5 ADJOINTS 8.6 UNITARY AND ORTHOGONAL OPERATORS 8.7 NORMAL OPERATORS Bibliography Index Blank Page