Basics of Matrix Algebra for Statistics with R > 수학/통계학

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