Matrix algebra is one of those areas of mathematics that is of paramount importance to statisticians and data analysts in general. This second edition of Gentle’s popular textbook supplies the reader with relevant, updated, and essential topics in matrix algebra, specifically matrices with applications to statistics and data analysis.

The book is broadly divided into three parts. Part 1, “Linear Algebra” (chapters 1 through 7), covers matrix structure and notation; vectors and vector spaces; properties and operations on matrices, including eigenanalysis and orthogonality; matrix/vectors derivatives and integrals; matrix transformations (for example, Householder and Gram–Schmidt processes) and factorizations (for example, LU, LDU, QR, and Cholesky); solving linear systems; and evaluating eigenvalues and eigenvectors.

Part 2, “Applications in Data Analysis” (two chapters), discusses “special matrices” (for example, positive definite matrices, Gramian matrices, projection and smoothing matrices, the generalized variance, Vandermonde matrices, Hadamard matrices, and Toeplitz matrices, to name a few) and “operations useful in modeling and data analysis.” This part also contains selected matrix applications in statistics, including multivariate statistical analysis, optimality design, and stochastic processes.

Part 3, “Numerical Methods and Software” (chapters 10 through 12), addresses numerical methods (for example, numerical algorithms and their analysis, efficiency, and errors; fixed- and floating-point representation, and so on), numerical linear algebra (for example, storage modes, sparsity, and general computations on vectors and matrices), and related programming languages and software (C, C++, Python, MATLAB, R, IMSL, and so on).

Although the book does not stick to any specific programming language or software, some working knowledge of programming in Fortran or C and an ability to use R or MATLAB could be useful to readers.

The second edition includes 100 new pages of exercises and discussion related to vectors and matrices, with additional complex elements and statistical applications. It also added user-friendly cross-references along with a helpful index. Although the omission of Amir Schoor’s algorithm for multiplying sparse matrices [1] surprised me, I enjoyed going through this lucidly written textbook and would definitely recommend it for advanced undergraduate and postgraduate students of mathematics, statistics, and computing sciences.