Basics of Matrix Algebra for Statistics with R

Nick Fieller

July 6, 2015 by Chapman and Hall/CRC
Reference - 248 Pages
ISBN 9781498712361 - CAT# K25114
Series: Chapman & Hall/CRC The R Series

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Features

  • Covers basic algebraic manipulation of matrices, such as basic arithmetic, inversion, partitioning, rank, determinants, decompositions, eigenanalysis, and Hadamard and Kronecker products
  • Shows how to implement the techniques in R using worked numerical examples
  • Describes vector and matrix calculus, including differentiation of scalars and linear and quadratic forms
  • Incorporates useful tricks, such as identifying rank 1 matrices and scalar subfactors within products
  • Explains how to convert an optimization problem to an eigenanalysis by imposing a non-restrictive constraint
  • Presents the derivation of key results in linear models and multivariate methods with step-by-step cross-referenced explanations
  • Includes numerous theoretical and numerical exercises for self-assessment

Summary

A Thorough Guide to Elementary Matrix Algebra and Implementation in R

Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject.

The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling.

In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers.

Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.