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

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Basics of Matrix Algebra for Statistics with R
판매가격 32,000원
저자 Fieller
도서종류 외국도서
출판사 CRC
발행언어 영어
발행일 2015-07
페이지수 248
ISBN 9781498712361
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  • 도서 정보

    도서 상세설명

    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
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