A Course in Linear Algebra with Applications / Edition 2

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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.

Numerous applications of linear algebra are described: these include systems of linear recurrence relations, systems of linear differential equations, Markov processes and the Method of Least Squares. In addition, an entirely new chapter on linear programming introduces the reader to the Simplex Algorithm and stresses understanding the theory on which the algorithm is based. The book is addressed to students who wish to learn linear algebra, as well as to professionals who need to use the methods of the subject in their own fields.

About the Author:
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

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Product Details

  • ISBN-13: 9789812700247
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 8/28/2006
  • Edition description: Second Edition
  • Edition number: 2
  • Pages: 452
  • Product dimensions: 6.05 (w) x 8.89 (h) x 0.90 (d)

Table of Contents

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