内容提要 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 PrefaceChapter 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 OperatorsPart 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 CalculusReferencesIndex of NotationIndex 作者介绍
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