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9789812700247

A Course in Linear Algebra With Applications

by
  • ISBN13:

    9789812700247

  • ISBN10:

    9812700242

  • Edition: 2nd
  • Format: Paperback
  • Copyright: 2006-08-30
  • Publisher: World Scientific Pub Co Inc
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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 Editionp. vii
Preface to the First Editionp. ix
Matrix Algebra
Matricesp. 1
Operations with Matricesp. 6
Matrices over Rings and Fieldsp. 24
Systems of Linear Equations
Gaussian Eliminationp. 30
Elementary Row Operationsp. 41
Elementary Matricesp. 47
Determinants
Permutations and the Definition of a Determinantp. 57
Basic Properties of Determinantsp. 70
Determinants and Inverses of Matricesp. 78
Introduction to Vector Spaces
Examples of Vector Spacesp. 87
Vector Spaces and Subspacesp. 95
Linear Independence in Vector Spacesp. 104
Basis and Dimension
The Existence of a Basisp. 112
The Row and Column Spaces of a Matrixp. 126
Operations with Subspacesp. 133
Linear Transformations
Functions Defined on Setsp. 152
Linear Transformations and Matricesp. 158
Kernel, Image and Isomorphismp. 178
Orthogonality in Vector Spaces
Scalar Products in Euclidean Spacep. 193
Inner Product Spacesp. 209
Orthonormal Sets and the Grain-Schmidt Processp. 206
The Method of Least Squaresp. 241
Eigenvectors and Eigenvalues
Basic Theory of Eigenvectors and Eigenvaluesp. 257
Applications to Systems of Linear Recurrencesp. 276
Applications to Systems of Linear Differential Equationsp. 288
More Advanced Topics
Eigenvalues and Eigenvectors of Symmetric and Hermitian Matricesp. 303
Quadratic Formsp. 313
Bilinear Formsp. 332
Minimum Polynomials and Jordan Normal Formp. 347
Linear Programming
Introduction to Linear Programmingp. 370
The Geometry of Linear Programmingp. 380
Basic Solutions and Extreme Pointsp. 391
The Simplex Algorithmp. 399
Mathematical Inductionp. 415
Answers to the Exercisesp. 418
Bibliographyp. 430
Indexp. 432
Table of Contents provided by Ingram. All Rights Reserved.

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