A Course in Linear Algebra With Applications

Derek J. S. Robinson9789812700230, 9812700234, 9812700242

Книга A Course in Linear Algebra With Applications A Course in Linear Algebra With Applications Книги Математика Автор: Derek J. S. Robinson Год издания: 2006 Формат: pdf Издат.:World Scientific Publishing Company Страниц: 452 Размер: 13 ISBN: 9812700234 Язык: Английский0 (голосов: 0) Оценка:The book is an introduction to Linear Algebra with an account of its principal applications. It is addressed to students of mathematics, the physical, engineering and social sciences, and commerce. The reader is assumed to have completed the calculus sequence. Special features of the book are thorough coverage of all core areas of linear algebra, with a detailed account of such important applications as least squares, systems of linear recurrences, Markov processes, and systems of differential equations. The book also gives an introduction to some more advanced topics such as diagonalization of Hermitian matrices and Jordan form. A principal aim of the book is to make the material accessible to the reader who is not a mathematician, without loss of mathematical rigor. This is reflected in a wealth of examples, the clarity of writing and the organization of material. There is a growing need for knowledge of linear algebra that goes beyond the basic skills of solving systems of linear equations and this book is intended to meet it.

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Table of contents :
CONTENTS……Page 14
Preface to the Second Edition……Page 8
Preface to the First Edition……Page 10
1.1 Matrices……Page 17
1.2 Operations with Matrices……Page 22
1.3 Matrices over Rings and Fields……Page 40
2.1 Gaussian Elimination……Page 46
2.2 Elementary Row Operations……Page 57
2.3 Elementary Matrices……Page 63
3.1 Permutations and the Definition of a Determinant……Page 73
3.2 Basic Properties of Determinants……Page 86
3.3 Determinants and Inverses of Matrices……Page 94
4.1 Examples of Vector Spaces……Page 103
4.2 Vector Spaces and Subspaces……Page 111
4.3 Linear Independence in Vector Spaces……Page 120
5.1 The Existence of a Basis……Page 128
5.2 The Row and Column Spaces of a Matrix……Page 142
5.3 Operations with Subspaces……Page 149
6.1 Functions Defined on Sets……Page 168
6.2 Linear Transformations and Matrices……Page 174
6.3 Kernel, Image and Isomorphism……Page 194
7.1 Scalar Products in Euclidean Space……Page 209
7.2 Inner Product Spaces……Page 225
7.3 Orthonormal Sets and the Gram-Schmidt Process……Page 242
7.4 The Method of Least Squares……Page 257
8.1 Basic Theory of Eigenvectors and Eigenvalues……Page 273
8.2 Applications to Systems of Linear Recurrences……Page 292
8.3 Applications to Systems of Linear Differential Equations……Page 304
9.1 Eigenvalues and Eigenvectors of Symmetric and Hermitian Matrices……Page 319
9.2 Quadratic Forms……Page 329
9.3 Bilinear Forms……Page 348
9.4 Minimum Polynomials and Jordan Normal Form……Page 363
10.1 Introduction to Linear Programming……Page 386
10.2 The Geometry of Linear Programming……Page 396
10.3 Basic Solutions and Extreme Points……Page 407
10.4 The Simplex Algorithm……Page 415
Appendix Mathematical Induction……Page 431
Answers to the Exercises……Page 434
Bibliography……Page 446
Index……Page 448