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An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapter-end practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Self-contained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott's research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.
Matrices --- Mathematical statistics --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal
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Mathematical statistics --- Matrices --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods
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"This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of non-negative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics."--
Matrices --- Eigenvalues --- Non-negative matrices --- Matrices. --- Eigenvalues. --- Non-negative matrices. --- Nonnegative matrices --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal
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This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of interest.
Mathematical statistics --- Matrices --- Business, Economy and Management --- Economics --- Matrices. --- Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Statistical methods
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Didactic evaluation --- Statistical science --- Mathematical statistics --- Sampling (Statistics) --- Matrices --- Random sampling --- Statistics of sampling --- Statistics --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Matrices. --- Sampling (Statistics).
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Ordered algebraic structures --- Semigroups. --- Matrices. --- Decomposition (Mathematics) --- Semi-groupes --- Matrices --- Décomposition (Mathématiques) --- 512 --- Semigroups --- Mathematics --- Probabilities --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Group theory --- Algebra --- Decomposition (Mathematics). --- 512 Algebra --- Décomposition (Mathématiques) --- Semigroupes
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Matrices --- Polynomials --- Polynômes --- 512.64 --- Algebra --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Linear and multilinear algebra. Matrix theory --- 512.64 Linear and multilinear algebra. Matrix theory --- Polynômes
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Matrices --- 512.64 --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Linear and multilinear algebra. Matrix theory --- Matrices. --- 512.64 Linear and multilinear algebra. Matrix theory
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Matrices --- #TCPW W2.0 --- #TCPW W2.2 --- 512.64 --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Linear and multilinear algebra. Matrix theory --- Matrices. --- 512.64 Linear and multilinear algebra. Matrix theory
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Transformations (Mathematics) --- Matrices --- 514.11 --- Algorithms --- Differential invariants --- Geometry, Differential --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Elementary geometry, trigonometry, polygonometry --- Matrices. --- Transformations (Mathematics). --- 514.11 Elementary geometry, trigonometry, polygonometry
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