A Course in Linear Algebra with Applications

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World Scientific, 2006 - Mathematics - 436 pages
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This is the second edition of the best-selling introduction to linear algebra. Presupposing no knowledge beyond calculus, it provides a thorough treatment of all the basic concepts, such as vector space, linear transformation and inner product. The concept of a quotient space is introduced and related to solutions of linear system of equations, and a simplified treatment of Jordan normal form is given.Numerous applications of linear algebra are described, including systems of linear recurrence relations, systems of linear differential equations, Markov processes, and the Method of Least Squares. An entirely new chapter on linear programing introduces the reader to the simplex algorithm with emphasis on understanding the theory behind it.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.
 

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Contents

Chapter One Matrix Algebra
1
Chapter Two Systems of Linear Equations
30
Chapter Three Determinants
57
Chapter Four Introduction to Vector Spaces
87
Chapter Five Basis and Dimension
112
Chapter Six Linear Transformations
152
Chapter Seven Orthogonality in Vector Spaces
193
Chapter Eight Eigenvectors and Eigenvalues
257
Chapter Nine More Advanced Topics
303
Chapter Ten Linear Programming
370
Appendix Mathematical Induction
415
Bibliography
430
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