A Course in Linear Algebra With Applications

by Robinson, Derek J. S.

• ISBN13: 9789812700247
• ISBN10: 9812700242
• Edition: 2nd
• Format: Paperback
• Copyright: 2006-08-30
• Publisher: World Scientific Pub Co Inc

Summary

This book is a comprehensive introduction to linear algebra which presupposes no knowledge on the part of the reader beyond the calculus. It gives a thorough treatment of all the basic concepts, such as vector space, linear transformation and inner product. The book proceeds at a gentle pace, yet provides full proofs. The concept of a quotient space is introduced and is related to solutions of linear system of equations. Also a simplified treatment of Jordan normal form is given.

Author Biography

Derek J.S. Robinson held positions at the University of London, the National University of Singapore and the University of illinois at Urbana-Champaign, where he is currently Professor of Mathematics

Table of Contents

Preface to the Second Edition	p. vii
Preface to the First Edition	p. ix
Matrix Algebra
Matrices	p. 1
Operations with Matrices	p. 6
Matrices over Rings and Fields	p. 24
Systems of Linear Equations
Gaussian Elimination	p. 30
Elementary Row Operations	p. 41
Elementary Matrices	p. 47
Determinants
Permutations and the Definition of a Determinant	p. 57
Basic Properties of Determinants	p. 70
Determinants and Inverses of Matrices	p. 78
Introduction to Vector Spaces
Examples of Vector Spaces	p. 87
Vector Spaces and Subspaces	p. 95
Linear Independence in Vector Spaces	p. 104
Basis and Dimension
The Existence of a Basis	p. 112
The Row and Column Spaces of a Matrix	p. 126
Operations with Subspaces	p. 133
Linear Transformations
Functions Defined on Sets	p. 152
Linear Transformations and Matrices	p. 158
Kernel, Image and Isomorphism	p. 178
Orthogonality in Vector Spaces
Scalar Products in Euclidean Space	p. 193
Inner Product Spaces	p. 209
Orthonormal Sets and the Grain-Schmidt Process	p. 206
The Method of Least Squares	p. 241
Eigenvectors and Eigenvalues
Basic Theory of Eigenvectors and Eigenvalues	p. 257
Applications to Systems of Linear Recurrences	p. 276
Applications to Systems of Linear Differential Equations	p. 288
More Advanced Topics
Eigenvalues and Eigenvectors of Symmetric and Hermitian Matrices	p. 303
Quadratic Forms	p. 313
Bilinear Forms	p. 332
Minimum Polynomials and Jordan Normal Form	p. 347
Linear Programming
Introduction to Linear Programming	p. 370
The Geometry of Linear Programming	p. 380
Basic Solutions and Extreme Points	p. 391
The Simplex Algorithm	p. 399
Mathematical Induction	p. 415
Answers to the Exercises	p. 418
Bibliography	p. 430
Index	p. 432
Table of Contents provided by Ingram. All Rights Reserved.