Elementary Matrix Theory

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Courier Corporation, 1966 - Mathematics - 325 pages
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The usefulness of matrix theory as a tool in disciplines ranging from quantum mechanics to psychometrics is widely recognized, and courses in matrix theory are increasingly a standard part of the undergraduate curriculum.
This outstanding text offers an unusual introduction to matrix theory at the undergraduate level. Unlike most texts dealing with the topic, which tend to remain on an abstract level, Dr. Eves' book employs a concrete elementary approach, avoiding abstraction until the final chapter. This practical method renders the text especially accessible to students of physics, engineering, business and the social sciences, as well as math majors. Although the treatment is fundamental — no previous courses in abstract algebra are required — it is also flexible: each chapter includes special material for advanced students interested in deeper study or application of the theory.
The book begins with preliminary remarks that set the stage for the author's concrete approach to matrix theory and the consideration of matrices as hypercomplex numbers. Dr. Eves then goes on to cover fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, similarity and congruence. A final optional chapter considers matrix theory from a generalized or abstract viewpoint, extending it to arbitrary number rings and fields, vector spaces and linear transformations of vector spaces. The author's concluding remarks direct the interested student to possible avenues of further study in matrix theory, while an extensive bibliography rounds out the book.
Students of matrix theory will especially appreciate the many excellent problems (solutions not provided) included in each chapter, which are not just routine calculation exercises, but involve proof and extension of the concepts and material of the text. Scientists, engineers, economists and others whose work involves this important area of mathematics, will welcome the variety of special types of matrices and determinants discussed, which make the book not only a comprehensive introduction to the field, but a valuable resource and reference work.

 

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It's interesting that this book, published in 1966, states that it is for undergraduates since much of this material would now (in 2010) be more likely to appear in a second course in linear algebra. The author writes clearly and this book is a great source of information beyond the introductory material in a modern linear algebra course. I'm not sure where some of this same material can be found in more recently published books. See also Matrices and Linear Transformations, 2nd ed, by Charles Cullen. 

Contents

PROLEGOMENON
1
FUNDAMENTAL CONCEPTS
14
ADDENDA
43
5A ENUMERATION OF fcSTAGE ROUTES
49
8A SQUARE ROOTS OF MATRICES
56
PROBLEMS
68
PROBLEMS
74
PROBLEMS
84
ADDENDA
160
10A QUANTITATIVE ASPECT OF LINEAR
174
ADDENDA
217
PROBLEMS
230
PROBLEMS
237
PROBLEMS
245
PROBLEMS
252
PROBLEMS
258

PROBLEMS
90
PROBLEMS
97
4A LINES IN A PLANE AND PLANES IN SPACE
103
DETERMINANTS
109
2A REGULAR SYMMETRIC MATRICES
264
TOWARD ABSTRACTION
276
EPILEGOMENON
307
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About the author (1966)

Howard Eves spent most of his teaching career at the University of Maine at Orono, and more recently at Central Florida University. For 25 years, he edited the Elementary Problems Section of the American Mathematical Monthly. His books include: Great Moments in Mathematics Before 1650, Mathematical Reminiscences, Introduction to the History of Mathematics, and his two-volume Survey of Geometry.

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