A course in linear algebra with applications / Derek J.S. Robinson.

Format:

Book

Author/Creator:

Robinson, Derek John Scott.

Contributor:

George R. Fink Memorial Fund.

Language:

English

Subjects (All):

Algebras, Linear.

Physical Description:

xv, 436 pages : illustrations ; 23 cm

Edition:

Second edition.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, [2006]

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.

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. Book jacket.

Contents:

Chapter 1 Matrix Algebra

1.1 Matrices 1

1.2 Operations with Matrices 6

1.3 Matrices over Rings and Fields 24

Chapter 2 Systems of Linear Equations

2.1 Gaussian Elimination 30

2.2 Elementary Row Operations 41

2.3 Elementary Matrices 47

Chapter 3 Determinants

3.1 Permutations and the Definition of a Determinant 57

3.2 Basic Properties of Determinants 70

3.3 Determinants and Inverses of Matrices 78

4.1 Examples of Vector Spaces 87

4.2 Vector Spaces and Subspaces 95

4.3 Linear Independence in Vector Spaces 104

Chapter 5 Basis and Dimension

5.1 The Existence of a Basis 112

5.2 The Row and Column Spaces of a Matrix 126

5.3 Operations with Subspaces 133

Chapter 6 Linear Transformations

6.1 Functions Defined on Sets 152

6.2 Linear Transformations and Matrices 158

6.3 Kernel, Image and Isomorphism 178

Chapter 7 Orthogonality in Vector Spaces

7.1 Scalar Products in Euclidean Space 193

7.2 Inner Product Spaces 209

7.3 Orthonormal Sets and the Grain-Schmidt Process 206

7.4 The Method of Least Squares 241

Chapter 8 Eigenvectors and Eigenvalues

8.1 Basic Theory of Eigenvectors and Eigenvalues 257

8.2 Applications to Systems of Linear Recurrences 276

8.3 Applications to Systems of Linear Differential Equations 288

Chapter 9 More Advanced Topics

9.1 Eigenvalues and Eigenvectors of Symmetric and Hermitian Matrices 303

9.2 Quadratic Forms 313

9.3 Bilinear Forms 332

9.4 Minimum Polynomials and Jordan Normal Form 347

Chapter 10 Linear Programming

10.2 The Geometry of Linear Programming 380

10.3 Basic Solutions and Extreme Points 391

10.4 The Simplex Algorithm 399

Appendix Mathematical Induction 415.

Notes:

Includes bibliographical references (pages 430-431) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the George R. Fink Memorial Fund.

ISBN:

9812700234

9812700242

9789812700230

OCLC:

76807476