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Record Nr. |
UNINA9910830523203321 |
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Autore |
Seber G. A. F (George Arthur Frederick), <1938-> |
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Titolo |
A matrix handbook for statisticians [[electronic resource] /] / George A.F. Seber |
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Pubbl/distr/stampa |
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Hoboken, N.J., : Wiley-Interscience, c2008 |
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ISBN |
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1-281-22179-1 |
9786611221799 |
0-470-22679-X |
0-470-22678-1 |
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Descrizione fisica |
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1 online resource (592 p.) |
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Collana |
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Wiley series in probability and statistics |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 529-545) and index. |
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Nota di contenuto |
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A MATRIX HANDBOOK FOR STATISTICIANS; CONTENTS; 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 Functions2.6 Coordinate Geometry; 2.6.1 Hyperplanes and Lines; 2.6.2 Quadratics; 2.6.3 Areas and Volumes; 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 and Patterned 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; |
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4.6 Norms |
4.6.1 Vector Norms4.6.2 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 Eigenvectors6.1.6 Hermitian Matrices; 6.1.7 Computational Methods; 6.1.8 Generalized Eigenvalues; 6.1.9 Matrix Products; 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 of Matrices; 7.2.3 Sums and Differences of Matrices; 7.2.4 Real Symmetric Matrices; 7.2.5 Decomposition Methods; 7.3 Other Inverses |
7.3.1 Reflexive (g12) Inverse7.3.2 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 of Matrices; 7.4.3 Products of Matrices; 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 |
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Sommario/riassunto |
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A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications 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 contain |
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