Linear Algebra And Its Applications, by David C. Lay

I’m not going to lie; this was a very boring book.  In all fairness, the book is a college level textbook in linear algebra, and few people would read such a book for their personal amusement as I did, so I will not judge it too harshly or not being particularly exciting, because I had no expectations that it would be so.  That said, this book does have ambitions of being relevant, if not exciting, and it is certainly intriguing and worthwhile to see how it is that the book encourages readers to pay attention to the relevance of its subjects, even if that subject is not the most exciting or interesting thing in the world.  Although this textbook seems to be the sort of book that the Manga Guide to Linear Algebra was written in response to, but all the same it is worthwhile to note that this book does try–very hard–to demonstrate the practical importance of linear algebra even if its approach is not very interesting and even if its style is particularly leaden.  It reminded me that knowledge of a subject’s relevance and a desire to convey the importance of subject matter is not sufficient to make something exciting to read.

This book is about 500 pages long and is divided into seven chapters.  The first chapter discusses linear equations in linear algebra, introducing the book’s concepts (1), which takes up the first 100 pages or so.  After that the author discusses matrix algebra, with plenty of problems to help the student master the material (2).  A short chapter on determinants follows, which includes Cramer’s rule (3), before the author moves on to discuss vector spaces and questions of rank and various applications (4) of the subject.  This leads into a chapter on eigenvalues and eigenvectors that shows applications to differential equations and spotted owls (5).  The author then concludes the main section of the book with a chapter on orthogonality and the least squares method (6) that provides plenty of applications and then a closing chapter on symmetric matrices and quadratic forms that deals with constraint optimization and other applications (7).  After this there are appendices on the uniqueness of the reduced echelon form (A) as well as complex numbers (B) for those who want additional material on these subjects, before the book concludes with a glossary, answers to odd-numbered exercises, and an index of the book’s materials.

In reading a book like this, even if I have no particular driving need to familiarize myself with linear algebra, I was reminded of the sort of appeal which teachers and textbook writers often use when it comes to mathematics subjects, and that is the push towards pointing out the applications of subjects.  To be sure, there are many applications of linear algebra and it is a very useful subject, as are many aspects of math and science and related subjects.  It was striking, though, to wonder why it was that the author of this book did not seek to inspire a certain degree of passion or creativity when it comes to the subject.  It is one thing to know that there are many ways to use a subject and many jobs where a given subject comes in handy, but it is an entirely different thing to be filled with a degree of passion and enthusiasm to solve particular problems in the world today through mastery of a technical field like linear algebra.  Contrary to this book’s overwhelming dullness (and reading it was I was falling asleep was certainly a very bad idea), this subject is worth more than just attempts to cure insomnia.