9780387964126

Linear Algebra

Serge A. Lang

3rd Edition

"Linear Algebra" is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, tri

5-1

Scalar Products

Exercises

p.103

5-2

Orthogonal Bases, Positive Definite Case

Exercises

p.111

5-3

Application to Linear Equations; The Rank

Exercises

p.117

5-4

bilinear Maps and Matrices

Exercises

p.122

5-5

General Orthogonal Bases

Exercises

p.125

5-6

The Dual Space and Scalar Products

Exercises

p.131

5-7

Quadratic Forms

Exercises

p.134

5-8

Sylvester's Theorem

Exercises

p.138

6-2

Existence of Determinants

Exercises

p.150

6-3

Additional Properties of Determinants

Exercises

p.154

6-4

Cramer's Rule

Exercises

p.160

6-5

Triangulation of a Matrix by Column Operations

Exercises

p.162

6-6

Permutations

Exercises

p.168

6-7

Expansion Formula and Uniqueness of Determinants

Exercises

p.173

6-8

Inverse of a Matrix

Exercises

p.177

6-9

The Rank of a Matrix and Subdeterminants

Exercises

p.179