Exercises in Numerical Linear Algebra and Matrix Factorizations

This is a companion volume to Lyche’s textbook (reviewed here) on numerical linear algebra and matrix factorization. It is tightly keyed to the original text and includes restatements of all the exercises from the book with complete solutions. 

 

The exercises vary considerably in levels of difficulty. For example, the first set includes an exercise to find the inverse of a 2x2 matrix and another to determine the operation count of a block matrix multiplication using Strassen’s fast matrix multiplication algorithm. As the book progresses to more advanced topics, the exercises continue to include a range of exercises from very straightforward to quite challenging.

 

More than 200 exercises are presented. Some of them use MATLAB code for solutions (with versions in Python provided online). The quality of solutions is very high. The authors take pains to write the solutions in some detail and they serve as effective teaching tools.

 

This combination of this book of exercises and solutions with the original book makes the text more approachable, and the additional teaching present in the solutions is quite valuable. It is not clear how an instructor might use these books in combination. Making full solutions of all exercises available to students immediately is, of course, problematic. Perhaps the best use of these two books in combination would be for students studying the subject independently.

 

This book of exercises and solutions would also be useful to instructors teaching a linear algebra course at a comparable level. There are a lot of good exercises here that would supplement those in other texts.

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Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.