Matrix Algebra for Linear Models

Detalles Bibliográficos
Autor principal: Gruber, Marvin H. J.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2013.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Matrix Algebra for Linear Models
  • Copyright
  • Contents
  • Preface
  • Acknowledgments
  • Part I Basic Ideas about Matrices and Systems of Linear Equations
  • Section 1 What Matrices Are and Some Basic Operations with Them
  • 1.1 Introduction
  • 1.2 What Are Matrices and Why Are They Interesting to a Statistician?
  • 1.3 Matrix Notation, Addition, and Multiplication
  • 1.4 Summary
  • Exercises
  • Section 2 Determinants and Solving a System of Equations
  • 2.1 Introduction
  • 2.2 Definition of and Formulae for Expanding Determinants
  • 2.3 Some Computational Tricks for the Evaluation of Determinants
  • 2.4 Solution to Linear Equations Using Determinants
  • 2.5 Gauss Elimination
  • 2.6 Summary
  • Exercises
  • Section 3 The Inverse of a Matrix
  • 3.1 Introduction
  • 3.2 The Adjoint Method of Finding the Inverse of a Matrix
  • 3.3 Using Elementary Row Operations
  • 3.4 Using the Matrix Inverse to Solve a System of Equations
  • 3.5 Partitioned Matrices and Their Inverses
  • 3.6 Finding the Least Square Estimator
  • 3.7 Summary
  • Exercises
  • Section 4 Special Matrices and Facts about Matrices That Will Be Used in the Sequel
  • 4.1 Introduction
  • 4.2 Matrices of the Form aIn+bJ n
  • 4.3 Orthogonal Matrices
  • 4.4 Direct Product of Matrices
  • 4.5 An Important Property of Determinants
  • 4.6 The Trace of a Matrix
  • 4.7 Matrix Differentiation
  • 4.8 The Least Square Estimator Again
  • 4.9 Summary
  • Exercises
  • Section 5 Vector Spaces
  • 5.1 Introduction
  • 5.2 What Is a Vector Space?
  • 5.3 The Dimension of a Vector Space
  • 5.4 Inner Product Spaces
  • 5.5 Linear Transformations
  • 5.6 Summary
  • Exercises
  • Section 6 The Rank of a Matrix and Solutions to Systems of Equations
  • 6.1 Introduction
  • 6.2 The Rank of a Matrix
  • 6.3 Solving Systems of Equations with Coefficient Matrix of Less than Full Rank
  • 6.4 Summary
  • Exercises
  • Part II Eigenvalues, the Singular Value Decomposition, and Principal Components
  • Section 7 Finding the Eigenvalues of a Matrix
  • 7.1 Introduction
  • 7.2 Eigenvalues and Eigenvectors of a Matrix
  • 7.3 Nonnegative Definite Matrices
  • 7.4 Summary
  • Exercises
  • Section 8 The Eigenvalues and Eigenvectors of Special Matrices
  • 8.1 Introduction
  • 8.2 Orthogonal, Nonsingular, and Idempotent Matrices
  • 8.3 The Cayley-Hamilton Theorem
  • 8.4 The Relationship between the Trace, the Determinant, and the Eigenvalues of a Matrix
  • 8.5 The Eigenvalues and Eigenvectors of the Kronecker Product of Two Matrices
  • 8.6 The Eigenvalues and the Eigenvectors of a Matrix of the Form aI + bJ
  • 8.7 The Loewner Ordering
  • 8.8 Summary
  • Exercises
  • Section 9 The Singular Value Decomposition (SVD)
  • 9.1 Introduction
  • 9.2 The Existence of the SVD
  • 9.3 Uses and Examples of the SVD
  • 9.4 Summary
  • Exercises
  • Section 10 Applications of the Singular Value Decomposition
  • 10.1 Introduction

Ejemplares similares