Basics of Matrix Algebra for Statistics with R (Hardcover)

· 제목 : Basics of Matrix Algebra for Statistics with R (Hardcover) 
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 대수학 일반
· ISBN : 9781498712361
· 쪽수 : 244쪽
· 출판일 : 2015-07-06

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

Index

Exercises appear at the end of each chapter.