Linear Algebra, Theory And Applications
Kenneth Kuttler, Bringham Young University
Copyright Year: 2012
Publisher: Saylor Foundation
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Conditions of Use
This is intended as a text for a second linear algebra course. In addition to covering the expected topics (in no particular order: linear transformations, matrices, row reduction, determinants, characteristic polynomial, spectral theory), the... read more
This is intended as a text for a second linear algebra course. In addition to covering the expected topics (in no particular order: linear transformations, matrices, row reduction, determinants, characteristic polynomial, spectral theory), the text starts with a chapter which could be used as a text for a course on the foundations of mathematics and it ends with chapters on analysis and algebra/number theory. The text includes an index.
The text is quite carefully written.
The text is likely to be useful to students beyond this course as a reference. In many cases, it anticipates more general results and sets up the statement of results in R^n to mirror those more general results.
Overall, the text is well-written. The author spends time introducing terminology. The only fault I find is the repeated editorializing, which is the author talking to the professor not the student.
The text is consistent in its use of terminology and notation.
The book has a clear skeleton which covers the content of a second course in linear algebra, along with more than enough material to add in as needed.
The text is coherent and largely well-organized. However, I would not introduce determinants before row operations and factorizations.
The text is easily viewed in a pdf reader.
There are no grammatical errors.
There are no obvious examples of offensive or insensitive material in the text.
The author is to be commended for his work. He has clearly devoted a substantial amount of time and energy in preparing a text that is well-structured, easy to read, and free of typographical errors.
Table of Contents
- Linear Transformations
- Row Operations
- Some Factorizations
- Spectral Theory
- Vector Spaces And Fields
- Linear Transformations
- Canonical Forms
- Markov Processes
- Inner Product Spaces
- Self Adjoint Operators
- Numerical Methods, Eigenvalues
About the Book
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.
This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants.
The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.
About the Contributors
Kenneth Kuttler, Professor of Mathematics at Bringham Young University. University of Texas at Austin, Ph.D. in Mathematics.