# Linear Algebra, Theory And Applications

Kenneth Kuttler, Bringham Young University

Copyright Year: 2012

Publisher: Saylor Foundation

Language: English

## Formats Available

## Conditions of Use

Attribution-ShareAlike

CC BY-SA

## Reviews

The book has detailed explanations of many topics in linear algebra. The theorems and proofs are well phrased. There are lot of examples to support the theory. Many problems are provided for additional practice. read more

The book has detailed explanations of many topics in linear algebra. The theorems and proofs are well phrased. There are lot of examples to support the theory. Many problems are provided for additional practice.

Without having enough time to go through every section in detail, the book is error-free.

The content is very relevant. The application examples are well chosen to demonstrate the theory and will not be outdated.

The text is clear, well written. The notation is sometimes a bit cumbersome but the author tries to give the most general form which requires more complex notation.

The book is consistent and connected throughout.

Because of the internal consistency and connectivity it would be difficult to pick and choose the topics out of the order. Notation, definitions, and the theorems throughout the book are related.

The book is well organized by topics, prepares the reader for what is coming next.

No issues in navigating through the book.

No grammatical errors.

The text is not culturally insensitive in any way.

The book has very good approach to linear algebra. It covers many topics and there are a lot of great applications. The theorems and proofs are well presented. There is so much material in the book that it would be impossible to use it in a one semester LA undergraduate course. It can be used by someone interested in linear algebra topics as a self-study course or as a reference book.

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

- Preliminaries
- Linear Transformations
- Determinants
- Row Operations
- Some Factorizations
- Spectral Theory
- Vector Spaces And Fields
- Linear Transformations
- Canonical Forms
- Markov Processes
- Inner Product Spaces
- Self Adjoint Operators
- Norms
- Numerical Methods, Eigenvalues

## Ancillary Material

## 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

### Author

**Kenneth Kuttler,** Professor of Mathematics at Bringham Young University. University of Texas at Austin, Ph.D. in Mathematics.