This book is a thorough introduction to linear algebra, for the graduate or advanced undergraduate student. Prerequisites are limited to a knowledge of the basic properties of matrices and determinants. However, since we cover the basics of vector spaces and linear transformations rather rapidly, a prior course in linear algebra (even at the sophomore level), along with a certain measure of "mathematical maturity," is highly desirable.
目录
Preface Chapter 0 Preliminaries Part 1: Preliminaries Part 2: Algebraic Structures. Part 1 Basic Linear AIgebra Chapter 1 Vector Spaces Chapter 2 Linear Transformations Chapter 3 The Isomorphism Theorems Chapter 4 Modules Ⅰ Chapter 5 Modules Ⅱ Chapter 6 Modules over Principal Ideal Domains Chapter 7 The Structure of a Linear Operator Chapter 8 Eigenvalues and Eigenvectors Chapter 9 Real and Complex Inner Product Spaces Chapter 10 The Spectral Theorem for Normal Operators Part 2 Topics Chapter 11 Metric Vector Spaces Chapter 12 Metric Spaces Chapter 13 Hilbert Spaces Chapter 14 Tensor Products Chapter 15 Affine Geometry Chapter 16 The Umbral Calculus References Index of Notation Index
