Linear Algebra

Cover......Page 1
Copyright......Page 5
Contents......Page 6
Preface......Page 10
Preface to the Second Edition......Page 14
A Note to Students......Page 16
List of Symbols......Page 18
 1.2BASIC CONCEPTS......Page 20
 1.3 MATRIX OPERATIONS AND THEIR PROPERTIES......Page 34
 1.4 INVERTIBLE MATRICES......Page 46
 1.5 TRANSPOSE OF A MATRIX......Page 51
 1.6 PARTITION OF MATRICES; BLOCK MULTIPLICATION......Page 55
 1.7 GROUPS AND FIELDS......Page 64
 2.2 GAUSSIAN ELIMINATION......Page 68
 2.3 ELEMENTARY ROW OPERATIONS......Page 74
 2.4 ROW REDUCTION......Page 84
 2.5 INVERTIBLE MATRICES AGAIN......Page 96
 2.6 LU FACTORIZATION......Page 101
 2.7 DETERMINANT......Page 115
 3.1 INTRODUCTION......Page 133
 3.2 BASIC CONCEPTS......Page 134
 3.3 LINEAR INDEPENDENCE......Page 146
 3.4 BASIS AND DIMENSION......Page 154
 3.6 RANK OF A MATRIX......Page 166
 3.7 ORTHOGONALITY IN Rn......Page 182
 3.8 BASES OF SUBSPACES......Page 197
 3.9 QUOTIENT SPACE......Page 203
 4.2 BASIC CONCEPTS......Page 210
 4.3 ALGEBRA OF LINEAR MAPS......Page 223
 4.4 ISOMORPHISM......Page 234
 4.5 MATRICES OF LINEAR MAPS......Page 240
 5.1 INTRODUCTION......Page 256
 5.2 POLYNOMIALS OVER FIELDS......Page 257
 5.3 CHARACTERISTIC POLYNOMIALS AND EIGENVALUES......Page 262
 5.4 MINIMAL POLYNOMIAL......Page 290
 5.5 INVARIANT SUBSPACES......Page 302
 5.6 SOME BASIC RESULTS......Page 317
 5.7 REAL QUADRATIC FORMS......Page 329
 6.2 PRIMARY DECOMPOSITION THEOREM......Page 340
 6.3 JORDAN FORMS......Page 348
 7.2 BASIC CONCEPTS......Page 365
 7.3 LINEAR FUNCTIONALS AND DUAL SPACE......Page 374
 7.4 SYMMETRIC BILINEAR FORMS......Page 379
 7.5 GROUPS PRESERVING BILINEAR FORMS......Page 393
 8.2 HERMITIAN FORMS......Page 399
 8.3 INNER PRODUCT SPACE......Page 404
 8.4 GRAM–SCHMIDT ORTHOGONALIZATION PROCESS......Page 409
 8.5 ADJOINTS......Page 422
 8.6 UNITARY AND ORTHOGONAL OPERATORS......Page 428
 8.7 NORMAL OPERATORS......Page 435
Bibliography......Page 449
Index......Page 450
Blank Page......Page 17