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## Details

Genre/Form: | Statistics |
---|---|

Material Type: | Internet resource |

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
G A F Seber |

ISBN: | 9780471748694 0471748692 |

OCLC Number: | 144770091 |

Description: | xix, 559 pages ; 25 cm. |

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 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. |

Series Title: | Wiley series in probability and statistics. |

Responsibility: | George A.F. Seber. |

More information: |

### Abstract:

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.
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## Reviews

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"This book maintains its uniqueness among the competition through its extensive referencing to proofs and comprehensive coverage of topics not found in any other one book." (International Statistical Review, Dec 2008) "This is an authoritative and comprehensive reference that will be useful to researchers who need to use the results of matrix analysis in their work. It would also be a useful addition to the reference collection of any mathematical library." (MAA Review, March 2008) Read more...

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