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Elementary Matrix Algebra

Franz E. Hohn
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
John T. Saccoman
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Franz E. Hohn’s Elementary Matrix Algebra is another one of those hidden gems of mathematics kept in print by the good folks at Dover. The book is an outgrowth of a course on “Linear Transformations and Matrices” that he taught for many years at the University of Illinois.

The text is well-written, and the author’s conversational style sets the book up nicely for someone who is using this as a self-study guide in this area. There are numerous examples and exercises, and the book’s expository sections are peppered with phrases that call upon active participation by the reader, such as “can you prove…?” and “the reader should show…” If this level of rigor and interactivity is indicative of Hohn’s presentation style, then he must have been an excellent lecturer indeed.

The reader would be aided by some background in Abstract Algebra, and this book or the course it represents is not a substitute for a Linear Algebra course. Indeed, the author’s preface to this edition admits, “…this book will make a following, mature study of linear algebra a more rewarding experience than it might otherwise have been.” Indeed, while there is thorough treatment of vector spaces and linear independence, the inner product spaces and other applications so crucial to a Linear Algebra course are given very cursory treatment.

In fact, the lack of specific applications is one of the drawbacks of the text. This is partly because the third edition was originally published in 1973, four years before Hohn’s death. In addition, while the text is excellent for self-study, there are no solutions included for the book’s copious exercises.

The book is appropriate for advanced undergraduates or beginning graduate students who desire to learn some matrix theory outside of a standard linear algebra course. There are a good number of exercises and a conversational yet rigorous style that make it excellent for brushing up on matrix theory.

John T. Saccoman is Professor of Mathematics at Seton Hall University in South Orange, NJ.

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