A Course in Linear Algebra with Applications

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World Scientific, 1991 - Mathematics - 422 pages
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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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Contents

Chapter One Matrix Algebra
1
Chapter Two Systems of Linear Equations
35
Chapter Three Determinants
65
Chapter Four Introduction to Vector Spaces
101
Chapter Five Basis and Dimension
131
Chapter Six Linear Transformations
169
Chapter Seven Orthogonality in Vector Spaces
213
Chapter Eight Eigenvectors and Eigenvalues
287
Chapter Nine Some More Advanced Topics
335
Appendix Mathematical Induction
401
Index
415
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