Comprehensiveness rating: 5 read 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.
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.
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.