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Linear Algebra, Theory And Applications
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  • Title Linear Algebra, Theory And Applications
  • Author(s) Kenneth Kuttler
  • Publisher: World Scientific Publishing Company (May 5, 2014); eBook (April 10, 2015)
  • Hardcover 332 pages
  • eBook PDF (503 pages, 6 MB)
  • Language: English
  • ISBN-10: 9814590533
  • ISBN-13: 978-9814590532, 978-1304912794
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Book Description

This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. I think that the subject of linear algebra is likely the most significant topic discussed in undergraduate mathematics courses. Part of the reason for this is its usefulness in unifying so many different topics.

This book gives a self- contained treatment of linear algebra with many of its most important applications. It is very unusual if not unique in being an elementary book which does not neglect arbitrary fields of scalars and the proofs of the theorems. It will be useful for beginning students and also as a reference for graduate students and others who need an easy to read explanation of the important theorems of this subject. It presents a self- contained treatment of the algebraic treatment of linear differential equation which includes all proofs. It also contains many different proofs of the Cayley Hamilton theorem. Other applications include difference equations and Markov processes, the latter topic receiving a more thorough treatment than usual, including the theory of absorbing states. In addition it contains a complete introduction to the singular value decomposition and related topics like least squares and the pseudo-inverse.

Most major topics receive more than one discussion, one in the text and others being outlined in the exercises. The book also gives directions for using maple in performing many of the difficult algorithms.

Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. This is the point of view of this book, more than a presentation of linear algebra for its own sake. This is why there are numerous applications, some fairly unusual.

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