Linear Algebra, Theory And Applications

Reviewed by Aida Galeb, Assistant Teaching Professor, University of Massachusetts Lowell on 6/29/20

Comprehensiveness rating: 5 see less

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.

Content Accuracy rating: 5

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

Relevance/Longevity rating: 5

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 The application examples are well chosen to demonstrate the theory and will not be outdated.

Clarity rating: 4

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.

Consistency rating: 5

The book is consistent and connected throughout.

Modularity rating: 3

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.

Organization/Structure/Flow rating: 5

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

Interface rating: 5

No issues in navigating through the book.

Grammatical Errors rating: 5

No grammatical errors.

Cultural Relevance rating: 5

The text is not culturally insensitive in any way.

Comments

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.

Reviewed by Leo Butler, Associate Professor, North Dakota State University on 1/7/16

Comprehensiveness rating: 5 see less

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.

Content Accuracy rating: 5

The text is quite carefully written.

Relevance/Longevity rating: 5

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.

Clarity rating: 5

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.

Consistency rating: 5

The text is consistent in its use of terminology and notation.

Modularity rating: 5

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.

Organization/Structure/Flow rating: 4

The text is coherent and largely well-organized. However, I would not introduce determinants before row operations and factorizations.

Interface rating: 5

The text is easily viewed in a pdf reader.

Grammatical Errors rating: 5

There are no grammatical errors.

Cultural Relevance rating: 5

There are no obvious examples of offensive or insensitive material in the text.

Comments

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.