Introduction 1 I. Linear Algebra 4 1. The Linear Space with Real Multiplier Domain 4 2. Finite Dimensional Linear Spaces 10 3. Linear Mappings 13 4. Bilinear and Quadratic Functions 26 5. Multilincar Functions 41 6. Metrization of affine Space 56 II. Differential Calculus 74
This undergraduate textbook is written for a junior/senior level course on linear optimization. Unlike other texts, the treatment follows the "modified Moore method" approach in which examples and proof opportunities are worked into the text in order to encourage students to develop some of the content through their own experiments and arguments while they are reading the text. Additionally, the focus is on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them.
The subjects covered in some detail include normed linear spaces, functions of linear operators, the basic structures of quantum mechanics and an introduction to linear programming. Also discussed are Kahler's metric, the theory of Hilbert polynomials, and projective and affine geometries. This comprehensive volume is unusual in its extensive use of applications in physics to clarify each topic. This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics.
This book is a revised and up-dated fourth edition of a textbook designed for upper division courses in linear algebra. It includes the basic results on vector spaces over fields, determinants, the theory of a single linear transformation, and inner product spaces. While it does not presuppose an earlier course, many connections between linear algebra and calculus are worked into the discussion, making it best suited for students who have completed the calculus sequence.
The present book, stemmin g from the first four chap ters of the authors' Tensor Calculus (Moscow, 1969), constitutes a lucid and completely elementary introduction to linear algebra. The treatment is virtually self-contained. In fact, the mathematical background assumed on the part of the reader hardly exceeds a smattering of calculus and a casual acquaintance with determinants. A special merit of the book, reflecting its lineage, is its free use of tensor notation, in particular the Einstein summation convention.
