Basics of matrix algebra for statistics with R / Nick Fieller

"A Chapman & Hall Book."

Introduction Objectives Further Reading Guide to Notation An Outline Guide to R Inputting Data to R Summary of Matrix Operators in R Examples of R Commands Vectors and Matrices Vectors Matrices Matrix Arithmetic Transpose and Trace of Sums and Products Special Matrices Partitioned Matrices Algebraic Manipulation of matrices Useful Tricks Linear and Quadratic Forms Creating Matrices in R Matrix Arithmetic in R Initial Statistical Applications Rank of Matrices Introduction and Definitions Rank Factorization Rank Inequalities Rank in Statistics Determinants Introduction and Definitions Implementation in R Properties of Determinants Orthogonal Matrices Determinants of Partitioned Matrices A Key Property of Determinants Inverses Introduction and Definitions Properties Implementation in R Inverses of Patterned Matrices Inverses of Partitioned Matrices General Formulae Initial Applications Continued Eigenanalysis of Real Symmetric Matrices Introduction and Definitions Eigenvectors Implementation in R Properties of Eigenanalyses A Key Statistical Application: PCA Matrix Exponential Decompositions Eigenanalysis of Matrices with Special Structures Summary of Key Results Vector and Matrix Calculus Introduction Differentiation of a Scalar with Respect to a Vector Differentiation of a Scalar with Respect to a Matrix Differentiation of a Vector with Respect to a Vector Differentiation of a Matrix with Respect to a Scalar Use of Eigenanalysis in Constrained Optimization Further Topics Introduction Further Matrix Decompositions Generalized Inverses Hadamard Products Kronecker Products and the Vec Operator Key Applications to Statistics Introduction The Multivariate Normal Distribution Principal Component Analysis Linear Discriminant Analysis Canonical Correlation Analysis Classical Scaling Linear Models Outline Solutions to Exercises Bibliography IndexExercises appear at the end of each chapter.