Nick Fieller’s book *Basics of Matrix Algebra for Statistics with R* provides a concise and straightforward presentation of matrix algebra techniques that are commonly used in statistics. Furthermore, the book discusses how to implement numerical instances of these techniques using R. I would describe this book as a compendium of definitions and results on matrix algebra and R commands for carrying out corresponding calculations. If you have a need or desire to carry out matrix computations in R, then it is likely that here you will find the needed commands.

There are several nice features of *Basics of Matrix Algebra for Statistics with R*. Because of the organization of the book, it is very easy to find the R command for carrying out a specific matrix calculation. First off, the index is good. Second, there is a summary of many useful commands in the first chapter. Finally, in each section of the text, the R commands clearly stand out. These features make the book useful as a reference. In addition, the author provides helpful tips and tricks for working with R.

Another positive feature of this book is the applications to statistics. While many of the applications are mixed in with the chapters on specific matrix algebra techniques, there is also a single chapter devoted entirely to statistical applications.

Even though *Basics of Matrix Algebra for Statistics with R* appears most useful as a reference or quick guide for statistics related matrix calculations, the inclusion of exercises facilitates the use of this book as a course text. Each chapter contains a good number of exercises' solutions are outlined at the end of the text. There are both computational exercises and exercises of a more theoretical nature.

Finally, it is natural to compare this book with texts on applied or numerical linear algebra such as *Matrix Computations* by Golub and Van Loan or *Matrix Analysis* by Horn and Johnson. While *Basics of Matrix Algebra for Statistics with R* does share some content with such books, its aim is completely different. For instance, it does not develop a great deal of general theory, focusing rather on specific tricks and techniques that are common in statistical calculations involving matrices. Consider as an example Chapter 6, which discusses eigenvalues and eigenvectors but in a restricted way that is nevertheless appropriate in statistical applications. There are many other examples of this in the text. All things considered, *Basics of Matrix Algebra for Statistics with R* is conveniently organized, well-written and should prove very useful for the purposes it was designed for.

Jason M. Graham is an assistant professor in the department of mathematics at the University of Scranton, Scranton, Pennsylvania. His current professional interests are in teaching applied mathematics and mathematical biology, and collaborating with biologists specializing in the collective behavior of groups of organisms.