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Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.

Banach spaces. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Functions of complex variables --- Generalized spaces --- Topology

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Banach spaces --- Banach spaces. --- 51 <031> --- 51 <031> Mathematics--Encyclopedieën. Lexica --- Mathematics--Encyclopedieën. Lexica --- Functions of complex variables --- Generalized spaces --- Topology

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Algebras, Linear. --- Algebras, Linear --- #KOPO:Prof. R. Holvoet --- 512.64 --- 512.64 Linear and multilinear algebra. Matrix theory --- Linear and multilinear algebra. Matrix theory --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology

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Numerical linear algebra is one of the most important subjects in the field of statistical computing. Statistical methods in many areas of application require computations with vectors and matrices. This book describes accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. An understanding of numerical linear algebra requires basic knowledge both of linear algebra and of how numerical data are stored and manipulated in the computer. The book begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, matrix factorizations, matrix and vector norms, and other topics in linear algebra; hence, the book is essentially self- contained. The topics addressed in this book constitute the most important material for an introductory course in statistical computing, and should be covered in every such course. The book includes exercises and can be used as a text for a first course in statistical computing or as supplementary text for various courses that emphasize computations. James Gentle is University Professor of Computational Statistics at George Mason University. During a thirteen-year hiatus from academic work before joining George Mason, he was director of research and design at the world's largest independent producer of Fortran and C general-purpose scientific software libraries. These libraries implement many algorithms for numerical linear algebra. He is a Fellow of the American Statistical Association and member of the International Statistical Institute. He has held several national.

Algebra --- Numerical analysis --- Algebras, Linear. --- Linear models (Statistics) --- Algèbre linéaire --- Modèles linéaires (Statistique) --- 519.61 --- Numerical methods of algebra --- 519.61 Numerical methods of algebra --- Algèbre linéaire --- Modèles linéaires (Statistique) --- Algebras, Linear --- Models, Linear (Statistics) --- Mathematical models --- Mathematical statistics --- Statistics --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- lineaire algebra --- Algebra. --- Statistics . --- Matrix theory. --- Statistics and Computing/Statistics Programs. --- Linear and Multilinear Algebras, Matrix Theory. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics