{"product_id":"matrix-algebra-useful-for-statistics-isbn-9781118935149","title":"Matrix Algebra Useful for Statistics","description":"\u003cp\u003e\u003cb\u003eA thoroughly updated guide to matrix algebra and it uses in statistical analysis and features SAS®, MATLAB®, and R throughout\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis \u003ci\u003eSecond Edition \u003c\/i\u003eaddresses 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 \u003ci\u003eSecond Edition \u003c\/i\u003ealso:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eContains new coverage on vector spaces and linear transformations and discusses computational aspects of matrices\u003c\/li\u003e \u003cli\u003eCovers the analysis of balanced linear models using direct products of matrices\u003c\/li\u003e \u003cli\u003eAnalyzes multiresponse linear models where several responses can be of interest\u003c\/li\u003e \u003cli\u003eIncludes extensive use of SAS, MATLAB, and R throughout\u003c\/li\u003e \u003cli\u003eContains over 400 examples and exercises to reinforce understanding along with select solutions\u003c\/li\u003e \u003cli\u003eIncludes plentiful new illustrations depicting the importance of geometry as well as historical interludes\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eMatrix Algebra Useful for Statistics, Second Edition \u003c\/i\u003eis 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.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eTHE LATE SHAYLE R. SEARLE, PHD, \u003c\/b\u003ewas professor emeritus of biometry at Cornell University. He was the author of \u003ci\u003eLinear Models for Unbalanced Data \u003c\/i\u003eand \u003ci\u003eLinear Models \u003c\/i\u003eand co-author of \u003ci\u003eGeneralized, Linear, and Mixed Models, Second Edition, Matrix Algebra for Applied Economics, \u003c\/i\u003eand \u003ci\u003eVariance Components, \u003c\/i\u003eall 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.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eANDRÉ I. KHURI, PHD, \u003c\/b\u003eis Professor Emeritus of Statistics at the University of Florida. He is the author of \u003ci\u003eAdvanced Calculus with Applications in Statistics, Second Edition \u003c\/i\u003eand co-author of \u003ci\u003eStatistical Tests for Mixed Linear Models, \u003c\/i\u003eall published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003ePreface to the First Edition xix\u003c\/p\u003e \u003cp\u003eIntroduction xxi\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Definitions, Basic Concepts, and Matrix Operations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Vector Spaces, Subspaces, and Linear Transformations 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Vector Spaces 3\u003c\/p\u003e \u003cp\u003e1.1.1 Euclidean Space 3\u003c\/p\u003e \u003cp\u003e1.2 Base of a Vector Space 5\u003c\/p\u003e \u003cp\u003e1.3 Linear Transformations 7\u003c\/p\u003e \u003cp\u003e1.3.1 The Range and Null Spaces of a Linear Transformation 8\u003c\/p\u003e \u003cp\u003eReference 9\u003c\/p\u003e \u003cp\u003eExercises 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Matrix Notation and Terminology 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Plotting of a Matrix 14\u003c\/p\u003e \u003cp\u003e2.2 Vectors and Scalars 16\u003c\/p\u003e \u003cp\u003e2.3 General Notation 16\u003c\/p\u003e \u003cp\u003eExercises 17\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Determinants 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Expansion by Minors 21\u003c\/p\u003e \u003cp\u003e3.1.1 First- and Second-Order Determinants 22\u003c\/p\u003e \u003cp\u003e3.1.2 Third-Order Determinants 23\u003c\/p\u003e \u003cp\u003e3.1.3 n-Order Determinants 24\u003c\/p\u003e \u003cp\u003e3.2 Formal Definition 25\u003c\/p\u003e \u003cp\u003e3.3 Basic Properties 27\u003c\/p\u003e \u003cp\u003e3.3.1 Determinant of a Transpose 27\u003c\/p\u003e \u003cp\u003e3.3.2 Two Rows the Same 28\u003c\/p\u003e \u003cp\u003e3.3.3 Cofactors 28\u003c\/p\u003e \u003cp\u003e3.3.4 Adding Multiples of a Row (Column) to a Row (Column) 30\u003c\/p\u003e \u003cp\u003e3.3.5 Products 30\u003c\/p\u003e \u003cp\u003e3.4 Elementary Row Operations 34\u003c\/p\u003e \u003cp\u003e3.4.1 Factorization 35\u003c\/p\u003e \u003cp\u003e3.4.2 A Row (Column) of Zeros 36\u003c\/p\u003e \u003cp\u003e3.4.3 Interchanging Rows (Columns) 36\u003c\/p\u003e \u003cp\u003e3.4.4 Adding a Row to a Multiple of a Row 36\u003c\/p\u003e \u003cp\u003e3.5 Examples 37\u003c\/p\u003e \u003cp\u003e3.6 Diagonal Expansion 39\u003c\/p\u003e \u003cp\u003e3.7 The Laplace Expansion 42\u003c\/p\u003e \u003cp\u003e3.8 Sums and Differences of Determinants 44\u003c\/p\u003e \u003cp\u003e3.9 A Graphical Representation of a 3 × 3 Determinant 45\u003c\/p\u003e \u003cp\u003eReferences 46\u003c\/p\u003e \u003cp\u003eExercises 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Matrix Operations 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The Transpose of a Matrix 51\u003c\/p\u003e \u003cp\u003e4.1.1 A Reflexive Operation 52\u003c\/p\u003e \u003cp\u003e4.1.2 Vectors 52\u003c\/p\u003e \u003cp\u003e4.2 Partitioned Matrices 52\u003c\/p\u003e \u003cp\u003e4.2.1 Example 52\u003c\/p\u003e \u003cp\u003e4.2.2 General Specification 54\u003c\/p\u003e \u003cp\u003e4.2.3 Transposing a Partitioned Matrix 55\u003c\/p\u003e \u003cp\u003e4.2.4 Partitioning Into Vectors 55\u003c\/p\u003e \u003cp\u003e4.3 The Trace of a Matrix 55\u003c\/p\u003e \u003cp\u003e4.4 Addition 56\u003c\/p\u003e \u003cp\u003e4.5 Scalar Multiplication 58\u003c\/p\u003e \u003cp\u003e4.6 Equality and the Null Matrix 58\u003c\/p\u003e \u003cp\u003e4.7 Multiplication 59\u003c\/p\u003e \u003cp\u003e4.7.1 The Inner Product of Two Vectors 59\u003c\/p\u003e \u003cp\u003e4.7.2 A Matrix–Vector Product 60\u003c\/p\u003e \u003cp\u003e4.7.3 A Product of Two Matrices 62\u003c\/p\u003e \u003cp\u003e4.7.4 Existence of Matrix Products 65\u003c\/p\u003e \u003cp\u003e4.7.5 Products With Vectors 65\u003c\/p\u003e \u003cp\u003e4.7.6 Products With Scalars 68\u003c\/p\u003e \u003cp\u003e4.7.7 Products With Null Matrices 68\u003c\/p\u003e \u003cp\u003e4.7.8 Products With Diagonal Matrices 68\u003c\/p\u003e \u003cp\u003e4.7.9 Identity Matrices 69\u003c\/p\u003e \u003cp\u003e4.7.10 The Transpose of a Product 69\u003c\/p\u003e \u003cp\u003e4.7.11 The Trace of a Product 70\u003c\/p\u003e \u003cp\u003e4.7.12 Powers of a Matrix 71\u003c\/p\u003e \u003cp\u003e4.7.13 Partitioned Matrices 72\u003c\/p\u003e \u003cp\u003e4.7.14 Hadamard Products 74\u003c\/p\u003e \u003cp\u003e4.8 The Laws of Algebra 74\u003c\/p\u003e \u003cp\u003e4.8.1 Associative Laws 74\u003c\/p\u003e \u003cp\u003e4.8.2 The Distributive Law 75\u003c\/p\u003e \u003cp\u003e4.8.3 Commutative Laws 75\u003c\/p\u003e \u003cp\u003e4.9 Contrasts With Scalar Algebra 76\u003c\/p\u003e \u003cp\u003e4.10 Direct Sum of Matrices 77\u003c\/p\u003e \u003cp\u003e4.11 Direct Product of Matrices 78\u003c\/p\u003e \u003cp\u003e4.12 The Inverse of a Matrix 80\u003c\/p\u003e \u003cp\u003e4.13 Rank of a Matrix—Some Preliminary Results 82\u003c\/p\u003e \u003cp\u003e4.14 The Number of LIN Rows and Columns in a Matrix 84\u003c\/p\u003e \u003cp\u003e4.15 Determination of the Rank of a Matrix 85\u003c\/p\u003e \u003cp\u003e4.16 Rank and Inverse Matrices 87\u003c\/p\u003e \u003cp\u003e4.17 Permutation Matrices 87\u003c\/p\u003e \u003cp\u003e4.18 Full-Rank Factorization 89\u003c\/p\u003e \u003cp\u003e4.18.1 Basic Development 89\u003c\/p\u003e \u003cp\u003e4.18.2 The General Case 91\u003c\/p\u003e \u003cp\u003e4.18.3 Matrices of Full Row (Column) Rank 91\u003c\/p\u003e \u003cp\u003eReferences 92\u003c\/p\u003e \u003cp\u003eExercises 92\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Special Matrices 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Symmetric Matrices 97\u003c\/p\u003e \u003cp\u003e5.1.1 Products of Symmetric Matrices 97\u003c\/p\u003e \u003cp\u003e5.1.2 Properties of AA′ and A′A 98\u003c\/p\u003e \u003cp\u003e5.1.3 Products of Vectors 99\u003c\/p\u003e \u003cp\u003e5.1.4 Sums of Outer Products 100\u003c\/p\u003e \u003cp\u003e5.1.5 Elementary Vectors 101\u003c\/p\u003e \u003cp\u003e5.1.6 Skew-Symmetric Matrices 101\u003c\/p\u003e \u003cp\u003e5.2 Matrices Having All Elements Equal 102\u003c\/p\u003e \u003cp\u003e5.3 Idempotent Matrices 104\u003c\/p\u003e \u003cp\u003e5.4 Orthogonal Matrices 106\u003c\/p\u003e \u003cp\u003e5.4.1 Special Cases 107\u003c\/p\u003e \u003cp\u003e5.5 Parameterization of Orthogonal Matrices 109\u003c\/p\u003e \u003cp\u003e5.6 Quadratic Forms 110\u003c\/p\u003e \u003cp\u003e5.7 Positive Definite Matrices 113\u003c\/p\u003e \u003cp\u003eReferences 114\u003c\/p\u003e \u003cp\u003eExercises 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Eigenvalues and Eigenvectors 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Derivation of Eigenvalues 119\u003c\/p\u003e \u003cp\u003e6.1.1 Plotting Eigenvalues 121\u003c\/p\u003e \u003cp\u003e6.2 Elementary Properties of Eigenvalues 122\u003c\/p\u003e \u003cp\u003e6.2.1 Eigenvalues of Powers of a Matrix 122\u003c\/p\u003e \u003cp\u003e6.2.2 Eigenvalues of a Scalar-by-Matrix Product 123\u003c\/p\u003e \u003cp\u003e6.2.3 Eigenvalues of Polynomials 123\u003c\/p\u003e \u003cp\u003e6.2.4 The Sum and Product of Eigenvalues 124\u003c\/p\u003e \u003cp\u003e6.3 Calculating Eigenvectors 125\u003c\/p\u003e \u003cp\u003e6.3.1 Simple Roots 125\u003c\/p\u003e \u003cp\u003e6.3.2 Multiple Roots 126\u003c\/p\u003e \u003cp\u003e6.4 The Similar Canonical Form 128\u003c\/p\u003e \u003cp\u003e6.4.1 Derivation 128\u003c\/p\u003e \u003cp\u003e6.4.2 Uses 130\u003c\/p\u003e \u003cp\u003e6.5 Symmetric Matrices 131\u003c\/p\u003e \u003cp\u003e6.5.1 Eigenvalues All Real 132\u003c\/p\u003e \u003cp\u003e6.5.2 Symmetric Matrices Are Diagonable 132\u003c\/p\u003e \u003cp\u003e6.5.3 Eigenvectors Are Orthogonal 132\u003c\/p\u003e \u003cp\u003e6.5.4 Rank Equals Number of Nonzero Eigenvalues for a Symmetric Matrix 135\u003c\/p\u003e \u003cp\u003e6.6 Eigenvalues of Orthogonal and Idempotent Matrices 135\u003c\/p\u003e \u003cp\u003e6.6.1 Eigenvalues of Symmetric Positive Definite and Positive Semidefinite Matrices 136\u003c\/p\u003e \u003cp\u003e6.7 Eigenvalues of Direct Products and Direct Sums of Matrices 138\u003c\/p\u003e \u003cp\u003e6.8 Nonzero Eigenvalues of AB and BA 140\u003c\/p\u003e \u003cp\u003eReferences 141\u003c\/p\u003e \u003cp\u003eExercises 141\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Diagonalization of Matrices 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Proving the Diagonability Theorem 145\u003c\/p\u003e \u003cp\u003e7.1.1 The Number of Nonzero Eigenvalues Never Exceeds Rank 145\u003c\/p\u003e \u003cp\u003e7.1.2 A Lower Bound on r (A − \u003ci\u003eλ\u003csub\u003ek\u003c\/sub\u003e\u003c\/i\u003eI) 146\u003c\/p\u003e \u003cp\u003e7.1.3 Proof of the Diagonability Theorem 147\u003c\/p\u003e \u003cp\u003e7.1.4 All Symmetric Matrices Are Diagonable 147\u003c\/p\u003e \u003cp\u003e7.2 Other Results for Symmetric Matrices 148\u003c\/p\u003e \u003cp\u003e7.2.1 Non-Negative Definite (n.n.d.) 148\u003c\/p\u003e \u003cp\u003e7.2.2 Simultaneous Diagonalization of Two Symmetric Matrices 149\u003c\/p\u003e \u003cp\u003e7.3 The Cayley–Hamilton Theorem 152\u003c\/p\u003e \u003cp\u003e7.4 The Singular-Value Decomposition 153\u003c\/p\u003e \u003cp\u003eReferences 157\u003c\/p\u003e \u003cp\u003eExercises 157\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Generalized Inverses 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Moore–Penrose Inverse 159\u003c\/p\u003e \u003cp\u003e8.2 Generalized Inverses 160\u003c\/p\u003e \u003cp\u003e8.2.1 Derivation Using the Singular-Value Decomposition 161\u003c\/p\u003e \u003cp\u003e8.2.2 Derivation Based on Knowing the Rank 162\u003c\/p\u003e \u003cp\u003e8.3 Other Names and Symbols 164\u003c\/p\u003e \u003cp\u003e8.4 Symmetric Matrices 165\u003c\/p\u003e \u003cp\u003e8.4.1 A General Algorithm 166\u003c\/p\u003e \u003cp\u003e8.4.2 The Matrix X′X 166\u003c\/p\u003e \u003cp\u003eReferences 167\u003c\/p\u003e \u003cp\u003eExercises 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Matrix Calculus 171\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Matrix Functions 171\u003c\/p\u003e \u003cp\u003e9.1.1 Function of Matrices 171\u003c\/p\u003e \u003cp\u003e9.1.2 Matrices of Functions 174\u003c\/p\u003e \u003cp\u003e9.2 Iterative Solution of Nonlinear Equations 174\u003c\/p\u003e \u003cp\u003e9.3 Vectors of Differential Operators 175\u003c\/p\u003e \u003cp\u003e9.3.1 Scalars 175\u003c\/p\u003e \u003cp\u003e9.3.2 Vectors 176\u003c\/p\u003e \u003cp\u003e9.3.3 Quadratic Forms 177\u003c\/p\u003e \u003cp\u003e9.4 Vec and Vech Operators 179\u003c\/p\u003e \u003cp\u003e9.4.1 Definitions 179\u003c\/p\u003e \u003cp\u003e9.4.2 Properties of Vec 180\u003c\/p\u003e \u003cp\u003e9.4.3 Vec-Permutation Matrices 180\u003c\/p\u003e \u003cp\u003e9.4.4 Relationships Between Vec and Vech 181\u003c\/p\u003e \u003cp\u003e9.5 Other Calculus Results 181\u003c\/p\u003e \u003cp\u003e9.5.1 Differentiating Inverses 181\u003c\/p\u003e \u003cp\u003e9.5.2 Differentiating Traces 182\u003c\/p\u003e \u003cp\u003e9.5.3 Derivative of a Matrix with Respect to Another Matrix 182\u003c\/p\u003e \u003cp\u003e9.5.4 Differentiating Determinants 183\u003c\/p\u003e \u003cp\u003e9.5.5 Jacobians 185\u003c\/p\u003e \u003cp\u003e9.5.6 Aitken’s Integral 187\u003c\/p\u003e \u003cp\u003e9.5.7 Hessians 188\u003c\/p\u003e \u003cp\u003e9.6 Matrices with Elements That Are Complex Numbers 188\u003c\/p\u003e \u003cp\u003e9.7 Matrix Inequalities 189\u003c\/p\u003e \u003cp\u003eReferences 193\u003c\/p\u003e \u003cp\u003eExercises 194\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Applications of Matrices in Statistics 199\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Multivariate Distributions and Quadratic Forms 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Variance-Covariance Matrices 202\u003c\/p\u003e \u003cp\u003e10.2 Correlation Matrices 203\u003c\/p\u003e \u003cp\u003e10.3 Matrices of Sums of Squares and Cross-Products 204\u003c\/p\u003e \u003cp\u003e10.3.1 Data Matrices 204\u003c\/p\u003e \u003cp\u003e10.3.2 Uncorrected Sums of Squares and Products 204\u003c\/p\u003e \u003cp\u003e10.3.3 Means, and the Centering Matrix 205\u003c\/p\u003e \u003cp\u003e10.3.4 Corrected Sums of Squares and Products 205\u003c\/p\u003e \u003cp\u003e10.4 The Multivariate Normal Distribution 207\u003c\/p\u003e \u003cp\u003e10.5 Quadratic Forms and χ\u003csup\u003e2\u003c\/sup\u003e-Distributions 208\u003c\/p\u003e \u003cp\u003e10.5.1 Distribution of Quadratic Forms 209\u003c\/p\u003e \u003cp\u003e10.5.2 Independence of Quadratic Forms 210\u003c\/p\u003e \u003cp\u003e10.5.3 Independence and Chi-Squaredness of Several Quadratic Forms 211\u003c\/p\u003e \u003cp\u003e10.5.4 The Moment and Cumulant Generating Functions for a Quadratic Form 211\u003c\/p\u003e \u003cp\u003e10.6 Computing the Cumulative Distribution Function of a Quadratic Form 213\u003c\/p\u003e \u003cp\u003e10.6.1 Ratios of Quadratic Forms 214\u003c\/p\u003e \u003cp\u003eReferences 215\u003c\/p\u003e \u003cp\u003eExercises 215\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Matrix Algebra of Full-Rank Linear Models 219\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Estimation of β by the Method of Least Squares 220\u003c\/p\u003e \u003cp\u003e11.1.1 Estimating the Mean Response and the Prediction Equation 223\u003c\/p\u003e \u003cp\u003e11.1.2 Partitioning of Total Variation Corrected for the Mean 225\u003c\/p\u003e \u003cp\u003e11.2 Statistical Properties of the Least-Squares Estimator 226\u003c\/p\u003e \u003cp\u003e11.2.1 Unbiasedness and Variances 226\u003c\/p\u003e \u003cp\u003e11.2.2 Estimating the Error Variance 227\u003c\/p\u003e \u003cp\u003e11.3 Multiple Correlation Coefficient 229\u003c\/p\u003e \u003cp\u003e11.4 Statistical Properties under the Normality Assumption 231\u003c\/p\u003e \u003cp\u003e11.5 Analysis of Variance 233\u003c\/p\u003e \u003cp\u003e11.6 The Gauss–Markov Theorem 234\u003c\/p\u003e \u003cp\u003e11.6.1 Generalized Least-Squares Estimation 237\u003c\/p\u003e \u003cp\u003e11.7 Testing Linear Hypotheses 237\u003c\/p\u003e \u003cp\u003e11.7.1 The Use of the Likelihood Ratio Principle in Hypothesis Testing 239\u003c\/p\u003e \u003cp\u003e11.7.2 Confidence Regions and Confidence Intervals 241\u003c\/p\u003e \u003cp\u003e11.8 Fitting Subsets of the x-Variables 246\u003c\/p\u003e \u003cp\u003e11.9 The Use of the R(.|.) Notation in Hypothesis Testing 247\u003c\/p\u003e \u003cp\u003eReferences 249\u003c\/p\u003e \u003cp\u003eExercises 249\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Less-Than-Full-Rank Linear Models 253\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 General Description 253\u003c\/p\u003e \u003cp\u003e12.2 The Normal Equations 256\u003c\/p\u003e \u003cp\u003e12.2.1 A General Form 256\u003c\/p\u003e \u003cp\u003e12.2.2 Many Solutions 257\u003c\/p\u003e \u003cp\u003e12.3 Solving the Normal Equations 257\u003c\/p\u003e \u003cp\u003e12.3.1 Generalized Inverses of X′X 258\u003c\/p\u003e \u003cp\u003e12.3.2 Solutions 258\u003c\/p\u003e \u003cp\u003e12.4 Expected Values and Variances 259\u003c\/p\u003e \u003cp\u003e12.5 Predicted y-Values 260\u003c\/p\u003e \u003cp\u003e12.6 Estimating the Error Variance 261\u003c\/p\u003e \u003cp\u003e12.6.1 Error Sum of Squares 261\u003c\/p\u003e \u003cp\u003e12.6.2 Expected Value 262\u003c\/p\u003e \u003cp\u003e12.6.3 Estimation 262\u003c\/p\u003e \u003cp\u003e12.7 Partitioning the Total Sum of Squares 262\u003c\/p\u003e \u003cp\u003e12.8 Analysis of Variance 263\u003c\/p\u003e \u003cp\u003e12.9 The R(⋅|⋅) Notation  265\u003c\/p\u003e \u003cp\u003e12.10 Estimable Linear Functions 266\u003c\/p\u003e \u003cp\u003e12.10.1 Properties of Estimable Functions 267\u003c\/p\u003e \u003cp\u003e12.10.2 Testable Hypotheses 268\u003c\/p\u003e \u003cp\u003e12.10.3 Development of a Test Statistic for \u003ci\u003eH\u003c\/i\u003e\u003csub\u003e0\u003c\/sub\u003e 269\u003c\/p\u003e \u003cp\u003e12.11 Confidence Intervals 272\u003c\/p\u003e \u003cp\u003e12.12 Some Particular Models 272\u003c\/p\u003e \u003cp\u003e12.12.1 The One-Way Classification 272\u003c\/p\u003e \u003cp\u003e12.12.2 Two-Way Classification, No Interactions, Balanced Data 273\u003c\/p\u003e \u003cp\u003e12.12.3 Two-Way Classification, No Interactions, Unbalanced Data 276\u003c\/p\u003e \u003cp\u003e12.13 The R(⋅|⋅) Notation (Continued)  277\u003c\/p\u003e \u003cp\u003e12.14 Reparameterization to a Full-Rank Model 281\u003c\/p\u003e \u003cp\u003eReferences 282\u003c\/p\u003e \u003cp\u003eExercises 282\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Analysis of Balanced Linear Models Using Direct Products of Matrices 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 General Notation for Balanced Linear Models 289\u003c\/p\u003e \u003cp\u003e13.2 Properties Associated with Balanced Linear Models 293\u003c\/p\u003e \u003cp\u003e13.3 Analysis of Balanced Linear Models 298\u003c\/p\u003e \u003cp\u003e13.3.1 Distributional Properties of Sums of Squares 298\u003c\/p\u003e \u003cp\u003e13.3.2 Estimates of Estimable Linear Functions of the Fixed Effects 301\u003c\/p\u003e \u003cp\u003eReferences 307\u003c\/p\u003e \u003cp\u003eExercises 308\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Multiresponse Models 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Multiresponse Estimation of Parameters 314\u003c\/p\u003e \u003cp\u003e14.2 Linear Multiresponse Models 316\u003c\/p\u003e \u003cp\u003e14.3 Lack of Fit of a Linear Multiresponse Model 318\u003c\/p\u003e \u003cp\u003e14.3.1 The Multivariate Lack of Fit Test 318\u003c\/p\u003e \u003cp\u003eReferences 323\u003c\/p\u003e \u003cp\u003eExercises 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Matrix Computations and Related Software 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 SAS\/IML 329\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Getting Started 329\u003c\/p\u003e \u003cp\u003e15.2 Defining a Matrix 329\u003c\/p\u003e \u003cp\u003e15.3 Creating a Matrix 330\u003c\/p\u003e \u003cp\u003e15.4 Matrix Operations 331\u003c\/p\u003e \u003cp\u003e15.5 Explanations of SAS Statements Used Earlier in the Text 354\u003c\/p\u003e \u003cp\u003eReferences 357\u003c\/p\u003e \u003cp\u003eExercises 358\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Use of MATLAB in Matrix Computations 363\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Arithmetic Operators 363\u003c\/p\u003e \u003cp\u003e16.2 Mathematical Functions 364\u003c\/p\u003e \u003cp\u003e16.3 Construction of Matrices 365\u003c\/p\u003e \u003cp\u003e16.3.1 Submatrices 365\u003c\/p\u003e \u003cp\u003e16.4 Two- and Three-Dimensional Plots 371\u003c\/p\u003e \u003cp\u003e16.4.1 Three-Dimensional Plots 374\u003c\/p\u003e \u003cp\u003eReferences 378\u003c\/p\u003e \u003cp\u003eExercises 379\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Use of R in Matrix Computations 383\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Two- and Three-Dimensional Plots 396\u003c\/p\u003e \u003cp\u003e17.1.1 Two-Dimensional Plots 397\u003c\/p\u003e \u003cp\u003e17.1.2 Three-Dimensional Plots 404\u003c\/p\u003e \u003cp\u003eReferences 408\u003c\/p\u003e \u003cp\u003eExercises 408\u003c\/p\u003e \u003cp\u003eAppendix 413\u003c\/p\u003e \u003cp\u003eIndex 475\u003c\/p\u003e \u003cp\u003e\"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.\" \u003cb\u003eMathematical Reviews, Sept 2017\u003c\/b\u003e\u003c\/p\u003e   \u003cp\u003e \u003cb\u003eThe late Shayle R. Searle, PhD,\u003c\/b\u003e was professor emeritus of biometry at Cornell University. He was the author of \u003ci\u003eLinear Models for Unbalanced Data\u003c\/i\u003e and \u003ci\u003eLinear Models\u003c\/i\u003e and co-author of \u003ci\u003eGeneralized, Linear, and Mixed Models, Second Edition, Matrix Algebra for Applied Economics, and Variance Components,\u003c\/i\u003e 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.  \u003c\/p\u003e\u003cp\u003e\u003cb\u003eAndré  I. Khuri, PhD,\u003c\/b\u003e is Professor Emeritus of Statistics at the University of Florida. He is the author of \u003ci\u003eAdvanced Calculus with Applications in Statistics, Second Edition\u003c\/i\u003e and co-author of \u003ci\u003eStatistical Tests for Mixed Linear Models,\u003c\/i\u003e 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.     \u003c\/p\u003e\u003cp\u003e \u003cb\u003eA thoroughly updated guide to matrix algebra and its uses in statistical analysis and features SAS®, MATLAB®, and R throughout\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e This \u003ci\u003eSecond Edition\u003c\/i\u003e 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 \u003ci\u003eSecond Edition\u003c\/i\u003e also:    \u003c\/p\u003e\u003cul\u003e \u003cli\u003eContains new coverage on vector spaces and linear transformations and discusses computational aspects of matrices\u003c\/li\u003e \u003cli\u003eCovers the analysis of balanced linear models using direct products of matrices\u003c\/li\u003e \u003cli\u003eAnalyzes multiresponse linear models where several responses can be of interest\u003c\/li\u003e \u003cli\u003eIncludes extensive use of SAS, MATLAB, and R throughout\u003c\/li\u003e \u003cli\u003eContains over 400 examples and exercises to reinforce understanding along with select solutions\u003c\/li\u003e \u003cli\u003eIncludes plentiful new illustrations depicting the importance of geometry as well as historical interludes \u003c\/li\u003e \u003c\/ul\u003e  \u003cp\u003e\u003ci\u003eMatrix Algebra Useful for Statistics, Second Edition\u003c\/i\u003e 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. \u003cbr\u003e\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989589573861,"sku":"NP9781118935149","price":116.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118935149.jpg?v=1761784716","url":"https:\/\/k12savings.com\/es\/products\/matrix-algebra-useful-for-statistics-isbn-9781118935149","provider":"K12savings","version":"1.0","type":"link"}