Fieller, N.: Basics of Matrix Algebra for Statistics with R

Abstract

Matrices are becoming more important than ever before in the big-data era of the modern multidimensional world.With advances in computing and statistical packages such as R, it has become easier to manipulate matrices and analyse data efficiently. The book begins with an introduction to R, including installation, functions and basic R commands and calculations. There follows a guide to basic matrix algebra in R with applications to statistics. It covers the major topics in matrix algebra including vectors, matrices, rank of matrices, determinants, inverses, eigenanalysis, matrix calculus and their key applications to statistics. The book also includes a chapter on advanced topics such as matrix decompositions, generalised inverses, and Hadamard and Kronecker products. Somewhat unfortunately, the book’s notation for matrix calculus is different from the notation advocated by Magnus and Neudecker (1999). The book also include tricks formanipulatingmatrices, plus derivation of key results with step-by-step cross-referenced explanations and demonstrations of the techniques in R using numerical examples. The chapter on key applications to statistics covers principal component analysis, linear discriminant analysis and canonical correlation analysis, in addition to linear models. Some chapters have a summary of key results which is useful for easy reference. End of chapter exercises are also available with solutions provided at the end of the book. The book avoids advanced mathematics and is therefore a good beginner’s guide to understanding and manipulating matrices in R. It is suitable for early year undergraduate students and anyone looking for an introduction to matrix algebra in R in preparation for high-level or specialised studies in statistics. The book’s collection of