Buch, Englisch, 512 Seiten, Format (B × H): 180 mm x 258 mm, Gewicht: 1021 g
Buch, Englisch, 512 Seiten, Format (B × H): 180 mm x 258 mm, Gewicht: 1021 g
Reihe: Wiley Series in Probability and Statistics
ISBN: 978-1-118-93514-9
Verlag: Wiley
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.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface xvii
Preface to the First Edition xix
Introduction xxi
About the Companion Website xxxi
Part I Definitions, Basic Concepts, and Matrix Operations 1
1 Vector Spaces, Subspaces, and Linear Transformations 3
1.1 Vector Spaces 3
1.1.1 Euclidean Space 3
1.2 Base of a Vector Space 5
1.3 Linear Transformations 7
1.3.1 The Range and Null Spaces of a Linear Transformation 8
Reference 9
Exercises 9
2 Matrix Notation and Terminology 11
2.1 Plotting of a Matrix 14
2.2 Vectors and Scalars 16
2.3 General Notation 16
Exercises 17
3 Determinants 21
3.1 Expansion by Minors 21
3.1.1 First- and Second-Order Determinants 22
3.1.2 Third-Order Determinants 23
3.1.3 n-Order Determinants 24
3.2 Formal Definition 25
3.3 Basic Properties 27
3.3.1 Determinant of a Transpose 27
3.3.2 Two Rows the Same 28
3.3.3 Cofactors 28
3.3.4 Adding Multiples of a Row (Column) to a Row (Column) 30
3.3.5 Products 30
3.4 Elementary Row Operations 34
3.4.1 Factorization 35
3.4.2 A Row (Column) of Zeros 36
3.4.3 Interchanging Rows (Columns) 36
3.4.4 Adding a Row to a Multiple of a Row 36
3.5 Examples 37
3.6 Diagonal Expansion 39
3.7 The Laplace Expansion 42
3.8 Sums and Differences of Determinants 44
3.9 A Graphical Representation of a 3 × 3 Determinant 45
References 46
Exercises 47
4 Matrix Operations 51
4.1 The Transpose of a Matrix 51
4.1.1 A Reflexive Operation 52
4.1.2 Vectors 52
4.2 Partitioned Matrices 52
4.2.1 Example 52
4.2.2 General Specification 54
4.2.3 Transposing a Partitioned Matrix 55
4.2.4 Partitioning Into Vectors 55
4.3 The Trace of a Matrix 55
4.4 Addition 56
4.5 Scalar Multiplication 58
4.6 Equality and the Null Matrix 58
4.7 Multiplication 59
4.7.1 The Inner Product of Two Vectors 59
4.7.2 A Matrix–Vector Product 60
4.7.3 A Product of Two Matrices 62
4.7.4 Existence of Matrix Products 65
4.7.5 Products With Vectors 65
4.7.6 Products With Scalars 68
4.7.7 Products With Null Matrices 68
4.7.8 Products With Diagonal Matrices 68
4.7.9 Identity Matrices 69
4.7.10 The Transpose of a Product 69
4.7.11 The Trace of a Product 70
4.7.12 Powers of a Matrix 71
4.7.13 Partitioned Matrices 72
4.7.14 Hadamard Products 74
4.8 The Laws of Algebra 74
4.8.1 Associative Laws 74
4.8.2 The Distributive Law 75
4.8.3 Commutative Laws 75
4.9 Contrasts With Scalar Algebra 76
4.10 Direct Sum of Matrices 77
4.11 Direct Product of Matrices 78
4.12 The Inverse of a Matrix 80
4.13 Rank of a Matrix—Some Preliminary Results 82
4.14 The Number of LIN Rows and Columns in a Matrix 84
4.15 Determination of the Rank of a Matrix 85
4.16 Rank and Inverse Matrices 87
4.17 Permutation Matrices 87
4.18 Full-Rank Factorization 89
4.18.1 Basic Development 89
4.18.2 The General Case 91
4.18.3 Matrices of Full Row (Column) Rank 91
References 92
Exercises 92
5 Special Matrices 97
5.1 Symmetric Matrices 97
5.1.1 Products of Symmetric Matrices 97
5.1.2 Properties of AA' and A'A 98
5.1.3 Products of Vectors 99
5.1.4 Sums of Outer Products 100
5.1.5 Elementary Vectors 101
5.1.6 Skew-Symmetric Matrices 101
5.2 Matrices Having All Elements Equal 102
5.3 Idempotent Matrices 104
5.4 Orthogonal Matrices 106
5.4.1 Special Cases 107
5.5 Parameterization of Orthogonal Matrices 109
5.6 Quadratic Forms 110
5.7 Positive Definite Matrices 113
References 114
Exercises 114
6 Eigenvalues and Eigenvectors 119
6.1 Der
