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Elementary Matrix Theory (Dover Books on Mathematics), by Howard Eves
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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.
- Sales Rank: #1518716 in eBooks
- Published on: 2012-04-30
- Released on: 2012-04-30
- Format: Kindle eBook
Most helpful customer reviews
59 of 64 people found the following review helpful.
Not Linear Algebra
By A Customer
I love this book. It contains a wealth of information on basic matrix theory that one almost never gets in the classroom or typical undergraduate texts. I never realised how rich the theory of matrix theory was until I read this book. Bare in mind, however, that this is not a text on linear algebra . . . the author does touch upon the subject, but even then it is linear algebra in the context of matrix theory and not matrices in the context of linear algebra. This is rather an old approach, but one I think that is very enlightening. The author touches on advanced topics such as Lie products, Hamilton products, tensor products and so on. I this way, the student learns that the traditional way of multiplying matrices is not the only way, but simply the way that linear algebra chooses to make use of the matrices. The level of the book is undegraduate, so that any intelligent high school student should be able to get much out of the book. No real math background is required, although it would be helpful. Theory is paid attention to, but a great deal of detail is also given worked out problems, making it ideal for math students who don't yet feel comfortable with advanced theoretical math.
3 of 5 people found the following review helpful.
Exelent clear writing
By Jorma Valkama
This is best mathematics book I've ever read. Eves presents his thoughts clearly and natural way, making it a comfortable reading experience.
The book has widened my understanding about matrixes.
0 of 2 people found the following review helpful.
Matrix Theory
By Allison Nelson
This was a purchase for my children as I like them to keep reading and learning to further their education. They enjoyed it.
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