Customer Reviews

Linear Algebra: Challenging Problems for Students (Johns Hopkins Studies in the Mathematical Sciences)

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Although the subtitle of the collection is "Challenging Problems for Students," a fair number of the problems are not difficult or tricky, but do a wonderful job of testing a student's understanding of the major concepts and techniques of elementary linear algebra. Not all of the problems are original, but they are all instructive and interesting. One of my favorites gives a product AB of a 3 x 2 and 2 x 3 matrix and asks for the product BA. The hints and solutions are clear and concise. I particularly appreciated the attractive layout of this text. Notation is chosen carefully, and everything from font size to spacing of text and the display of complex expressions seems to have been considered with utmost concern and respect for the reader. This book is a very good resource for both students and teachers of linear algebra.

Teachers of college mathematics are always long on stress and short on time. Exams come at regular intervals and finding the right problems to put on them is always a challenge. This is especially true for courses based on theory rather than algorithm execution. I have always found it easy to write exams in courses such as calculus, algebra and statistics, but find myself spending a lot of time creating the exams for courses such as linear and abstract algebra.
This book contains 200 problems and they are split into the following five categories:

1) Vector spaces
2) Determinants, inverses, rank and linear equations.
3) Matrices, linear transformations and eigenvalues.
4) Special matrices: Hadamard, Hermitian, Unitary, Normal and Permutation.
5) Inner product spaces.

While the problems are challenging, they are not unduly so and generally are within the range of what can be offered to your more talented students. Detailed hints to all of the problems are included.
If you are looking for problems to illustrate specific theoretical topics in linear algebra or need ideas for test problems, then this book is a resource that you should take a long look at. I am sure you will find something of value.

This expanded version contains a lot more practice problems plus review for basic linear algebra and matrix theory; it's an excellent book for math/stat majors and graduate students, especially for those who are to take "qualifying exams"...