Matrix Algebra Useful for Statistics, 2nd Edition
- Length: 512 pages
- Edition: 2
- Language: English
- Publisher: Wiley
- Publication Date: 2017-04-10
- ISBN-10: B06Y6DMXG5
- ISBN-13: 9781118935149
- Sales Rank: #1597783 (See Top 100 Books)
A thoroughly updated guide to matrix algebra and it uses in statistical analysis and features SAS®, MATLAB®, and R throughout
This Second Edition addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained. Featuring numerous applied illustrations, numerical examples, and exercises, the book has been updated to include the use of SAS, MATLAB, and R for the execution of matrix computations. In addition, André I. Khuri, who has extensive research and teaching experience in the field, joins this new edition as co-author. The Second Edition also:
- Contains new coverage on vector spaces and linear transformations and discusses computational aspects of matrices
- Covers the analysis of balanced linear models using direct products of matrices
- Analyzes multiresponse linear models where several responses can be of interest
- Includes extensive use of SAS, MATLAB, and R throughout
- Contains over 400 examples and exercises to reinforce understanding along with select solutions
- Includes plentiful new illustrations depicting the importance of geometry as well as historical interludes
Matrix Algebra Useful for Statistics, Second Edition is an ideal textbook for advanced undergraduate and first-year graduate level courses in statistics and other related disciplines. The book is also appropriate as a reference for independent readers who use statistics and wish to improve their knowledge of matrix algebra.
THE LATE SHAYLE R. SEARLE, PHD, was professor emeritus of biometry at Cornell University. He was the author of Linear Models for Unbalanced Data and Linear Models and co-author of Generalized, Linear, and Mixed Models, Second Edition, Matrix Algebra for Applied Economics, and Variance Components, all published by Wiley. Dr. Searle received the Alexander von Humboldt Senior Scientist Award, and he was an honorary fellow of the Royal Society of New Zealand.
ANDRÉ I. KHURI, PHD, is Professor Emeritus of Statistics at the University of Florida. He is the author of Advanced Calculus with Applications in Statistics, Second Edition and co-author of Statistical Tests for Mixed Linear Models, all published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.
Table of Contents
PART I DEFINITIONS, BASIC CONCEPTS, AND MATRIX OPERATIONS
Chapter 1 Vector Spaces, Subspaces, And Linear Transformations
Chapter 2 Matrix Notation And Terminology
Chapter 3 Determinants
Chapter 4 Matrix Operations
Chapter 5 Special Matrices
Chapter 6 Eigenvalues And Eigenvectors
Chapter 7 Diagonalization Of Matrices
Chapter 8 Generalized Inverses
Chapter 9 Matrix Calculus
PART II APPLICATIONS OF MATRICES IN STATISTICS
Chapter 10 Multivariate Distributions And Quadratic Forms
Chapter 11 Matrix Algebra Of Full-Rank Linear Models
Chapter 12 Less-Than-Full-Rank Linear Models
Chapter 13 Analysis Of Balanced Linear Models Using Direct Products Of Matrices
Chapter 14 Multiresponse Models
PART III MATRIX COMPUTATIONS AND RELATED SOFTWARE
Chapter 15 Sas/Iml
Chapter 16 Use Of Matlab In Matrix Computations
Chapter 17 Use Of R In Matrix Computations
PREFACE PREFACE TO THE FIRST EDITION INTRODUCTION ABOUT THE COMPANION WEBSITE PART I DEFINITIONS, BASIC CONCEPTS, AND MATRIX OPERATIONS 1 Vector Spaces, Subspaces, and Linear Transformations 1.1 Vector Spaces 1.2 Base of a Vector Space 1.3 Linear Transformations Reference Exercises 2 Matrix Notation and Terminology 2.1 Plotting of a Matrix 2.2 Vectors and Scalars 2.3 General Notation Exercises 3 Determinants 3.1 Expansion by Minors 3.2 Formal Definition 3.3 Basic Properties 3.4 Elementary Row Operations 3.5 Examples 3.6 Diagonal Expansion 3.7 The Laplace Expansion 3.8 Sums and Differences of Determinants 3.9 A Graphical Representation of a 3 × 3 Determinant Exercises Notes References 4 Matrix Operations 4.1 The Transpose of a Matrix 4.2 Partitioned Matrices 4.3 The Trace of a Matrix 4.4 Addition 4.5 Scalar Multiplication 4.6 Equality and the Null Matrix 4.7 Multiplication 4.8 The Laws of Algebra 4.9 Contrasts With Scalar Algebra 4.10 Direct Sum of Matrices 4.11 Direct Product of Matrices 4.12 The Inverse of a Matrix 4.13 Rank of a Matrix—Some Preliminary Results 4.14 The Number of LIN Rows and Columns in a Matrix 4.15 Determination of The Rank of a Matrix 4.16 Rank and Inverse Matrices 4.17 Permutation Matrices 4.18 Full-Rank Factorization Exercises References 5 Special Matrices 5.1 Symmetric Matrices 5.2 Matrices Having all Elements Equal 5.3 Idempotent Matrices 5.4 Orthogonal Matrices 5.5 Parameterization of Orthogonal Matrices 5.6 Quadratic Forms 5.7 Positive Definite Matrices Exercises References 6 Eigenvalues and Eigenvectors 6.1 Derivation of Eigenvalues 6.2 Elementary Properties of Eigenvalues 6.3 Calculating Eigenvectors 6.4 The Similar Canonical Form 6.5 Symmetric Matrices 6.6 Eigenvalues of orthogonal and Idempotent Matrices 6.7 Eigenvalues of Direct Products and Direct Sums of Matrices 6.8 Nonzero Eigenvalues of AB and BA Exercises Notes References 7 Diagonalization of Matrices 7.1 Proving the Diagonability Theorem 7.2 Other Results for Symmetric Matrices 7.3 The Cayley–Hamilton Theorem 7.4 The Singular-Value Decomposition Exercises References 8 Generalized Inverses 8.1 The Moore–Penrose Inverse 8.2 Generalized Inverses 8.3 Other Names and Symbols 8.4 Symmetric Matrices Exercises References 9 Matrix Calculus 9.1 Matrix Functions 9.2 Iterative Solution of Nonlinear Equations 9.3 Vectors of Differential Operators 9.4 Vec and Vech Operators 9.5 Other Calculus Results 9.6 Matrices With Elements That Are Complex Numbers 9.7 Matrix Inequalities Exercises Notes References PART II APPLICATIONS OF MATRICES IN STATISTICS 10 Multivariate Distributions and Quadratic Forms 10.1 Variance-Covariance Matrices 10.2 Correlation Matrices 10.3 Matrices of Sums of Squares and Cross-Products 10.4 The Multivariate Normal Distribution 10.5 Quadratic Forms and χ2-Distributions 10.6 Computing the Cumulative Distribution Function of a Quadratic Form Exercises References 11 Matrix Algebra of Full-Rank Linear Models 11.1 Estimation of β by the Method of Least Squares 11.2 Statistical Properties of the Least-Squares Estimator 11.3 Multiple Correlation Coefficient 11.4 Statistical Properties Under the Normality Assumption 11.5 Analysis of Variance 11.6 The Gauss–Markov Theorem 11.7 Testing Linear Hypotheses 11.8 Fitting Subsets of the x-Variables 11.9 The use of the R(.|.) Notation in Hypothesis Testing Exercises References 12 Less-Than-Full-Rank Linear Models 12.1 General Description 12.2 The Normal Equations 12.3 Solving the Normal Equations 12.4 Expected values and variances 12.5 Predicted y-Values 12.6 Estimating the Error Variance 12.7 Partitioning the Total Sum of Squares 12.8 Analysis of Variance 12.9 The R( · | · ) Notation 12.10 Estimable Linear Functions 12.11 Confidence Intervals 12.12 Some Particular Models 12.13 The R( · | ·) Notation (continued) 12.14 Reparameterization to a Full-Rank Model Exercises References 13 Analysis of Balanced Linear Models Using Direct Products of Matrices 13.1 General Notation for Balanced Linear Models 13.2 Properties Associated with Balanced Linear Models 13.3 Analysis of Balanced Linear Models References Exercises 14 Multiresponse Models 14.1 Multiresponse Estimation of Parameters 14.2 Linear Multiresponse Models 14.3 Lack of Fit of a Linear Multiresponse Model Exercises References PART III MATRIX COMPUTATIONS AND RELATED SOFTWARE 15 SAS/IML 15.1 Getting Started 15.2 Defining a Matrix 15.3 Creating a Matrix 15.4 Matrix Operations 15.5 Explanations of SAS Statements Used Earlier in the Text References Exercises 16 Use of MATLAB in Matrix Computations 16.1 Arithmetic Operators 16.2 Mathematical Functions 16.3 Construction of Matrices 16.4 Two- and Three-Dimensional Plots Exercises References 17 Use of R in Matrix Computations 17.1 Two- and Three-Dimensional Plots References Exercises APPENDIX SOLUTIONS TO EXERCISES Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 INDEX EULA
Donate to keep this site alive
1. Disable the AdBlock plugin. Otherwise, you may not get any links.
2. Solve the CAPTCHA.
3. Click download link.
4. Lead to download server to download.