http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Seber, G. A. F. (George Arthur Frederick)
"This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized." "Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers."--Jacket.
Preface. 1. Notation. 1.1 General Definitions. 1.2 Some Continuous Univariate Distributions. 1.3 Glossary of Notation. 2. Vectors, Vector Spaces, and Convexity. 2.1 Vector Spaces. 2.1.1 Definitions. 2.1.2 Quadratic Subspaces. 2.1.3 Sums and Intersections of Subspaces. 2.1.4 Span and Basis. 2.1.5 Isomorphism. 2.2 Inner Products. 2.2.1 Definition and Properties. 2.2.2 Functionals. 2.2.3 Orthogonality. 2.2.4 Column and Null Spaces. 2.3 Projections. 2.3.1 General Projections. 2.3.2 Orthogonal Projections. 2.4 Metric Spaces. 2.5 Convex Sets and Functions. 2.6 Coordinate Geometry. 2.6.1 Hyperplanes and Lines. 2.6.2 Quadratics. 2.6.3 Miscellaneous Results. 3. Rank. 3.1 Some General Properties. 3.2 Matrix Products. 3.3 Matrix Cancellation Rules. 3.4 Matrix Sums. 3.5 Matrix Differences. 3.6 Partitioned Matrices. 3.7 Maximal and Minimal Ranks. 3.8 Matrix Index. 4. Matrix Functions: Inverse, Transpose, Trace, Determinant, and Norm. 4.1 Inverse. 4.2 Transpose. 4.3 Trace. 4.4 Determinants. 4.4.1 Introduction. 4.4.2 Adjoint Matrix. 4.4.3 Compound Matrix. 4.4.4 Expansion of a Determinant. 4.5 Permanents. 4.6 Norms. 4.6.1 Vector Norms. 4.6.2 Matrix Norms. 4.6.3 Unitarily Invariant Norms. 4.6.4 M, N Invariant Norms. 4.6.5 Computational Accuracy. 5. Complex, Hermitian, and Related Matrices. 5.1 Complex Matrices. 5.1.1 Some General Results. 5.1.2 Determinants. 5.2 Hermitian Matrices. 5.3 Skew Hermitian Matrices. 5.4 Complex Symmetric Matrices. 5.5 Real Skew Symmetric Matrices. 5.6 Normal Matrices. 5.7 Quaternions. 6. Eigenvalues, Eigenvectors, and Singular Values. 6.1 Introduction and Definitions. 6.1.1 Characteristic Polynomial. 6.1.2 Eigenvalues. 6.1.3 Singular Values. 6.1.4 Functions of a Matrix. 6.1.5 Eigenvectors. 6.1.6 Hermitian Matrices. 6.1.7 Computational Methods. 6.1.8 Generalized Eigenvalues. 6.1.9 Matrix Products 103.6.2 Variational Characteristics for Hermitian Matrices. 6.3 Separation Theorems. 6.4 Inequalities for Matrix Sums. 6.5 Inequalities for Matrix Differences. 6.6 Inequalities for Matrix Products. 6.7 Antieigenvalues and Antieigenvectors. 7. Generalized Inverses. 7.1 Definitions. 7.2 Weak Inverses. 7.2.1 General Properties. 7.2.2 Products. 7.2.3 Sums and Differences. 7.2.4 Real Symmetric Matrices. 7.2.5 Decomposition Methods. 7.3 Other Inverses. 7.3.1 Reflexive (g12) Inverse. 7.3.2 Minimum Norm (g14) Inverse. 7.3.3 Minimum Norm Reflexive (g124) Inverse. 7.3.4 Least Squares (g13) Inverse. 7.3.5 Least Squares Reflexive (g123) Inverse. 7.4 Moore Penrose (g1234) Inverse. 7.4.1 General Properties. 7.4.2 Sums. 7.4.3 Products. 7.5 Group Inverse. 7.6 Some General Properties of Inverses. 8. Some Special Matrices. 8.1 Orthogonal and Unitary Matrices. 8.2 Permutation Matrices. 8.3 Circulant, Toeplitz, and Related Matrices. 8.3.1 Regular Circulant. 8.3.2 Symmetric Regular Circulant. 8.3.3 Symmetric Circulant. 8.3.4 Toeplitz Matrix. 8.3.5 Persymmetric Matrix. 8.3.6 Cross Symmetric (Centrosymmetric) Matrix. 8.3.7 Block Circulant. 8.3.8 Hankel Matrix. 8.4 Diagonally Dominant Matrices. 8.5 Hadamard Matrices. 8.6 Idempotent Matrices. 8.6.1 General Properties. 8.6.2 Sums o.
Includes bibliographical references (pages 529-545) and index.
Wiley series in probability and statistics