LEADER 05353nam 22006494a 450 001 9910145276203321 005 20170815115008.0 010 $a1-281-22179-1 010 $a9786611221799 010 $a0-470-22679-X 010 $a0-470-22678-1 035 $a(CKB)1000000000404457 035 $a(EBL)331465 035 $a(OCoLC)437198714 035 $a(SSID)ssj0000199328 035 $a(PQKBManifestationID)11204116 035 $a(PQKBTitleCode)TC0000199328 035 $a(PQKBWorkID)10184691 035 $a(PQKB)10083422 035 $a(MiAaPQ)EBC331465 035 $a(PPN)130975982 035 $a(EXLCZ)991000000000404457 100 $a20070612d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA matrix handbook for statisticians$b[electronic resource] /$fGeorge A.F. Seber 210 $aHoboken, N.J. $cWiley-Interscience$dc2008 215 $a1 online resource (592 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a0-471-74869-2 320 $aIncludes bibliographical references (p. 529-545) and index. 327 $aA 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 327 $a2.5 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; 4.6 Norms 327 $a4.6.1 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 327 $a6.1.5 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 327 $a7.3.1 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 327 $a8.3.4 Toeplitz Matrix 330 $aA comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contain 410 0$aWiley series in probability and statistics. 606 $aMatrices 606 $aStatistics 615 0$aMatrices. 615 0$aStatistics. 676 $a512.9/434 676 $a512.9434 700 $aSeber$b G. A. F$g(George Arthur Frederick),$f1938-$020688 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910145276203321 996 $aA matrix handbook for statisticians$92016789 997 $aUNINA