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Author: F. F. Bonsall Publisher: Cambridge University Press ISBN: 0521202272 Category : Mathematics Languages : en Pages : 189
Book Description
The landlady, landlord, cat, trap, and cheese all take credit for catching the long-tailed rat who is really the only one who knows the truth of the matter.
Author: F. F. Bonsall Publisher: Cambridge University Press ISBN: 0521202272 Category : Mathematics Languages : en Pages : 189
Book Description
The landlady, landlord, cat, trap, and cheese all take credit for catching the long-tailed rat who is really the only one who knows the truth of the matter.
Author: F. F. Bonsall Publisher: Cambridge University Press ISBN: 9780521079884 Category : Mathematics Languages : en Pages : 148
Book Description
The theory of the numerical range of a linear operator on an arbitrary normed space had its beginnings around 1960, and during the 1970s the subject has developed and expanded rapidly. This book presents a self-contained exposition of the subject as a whole. The authors develop various applications, in particular to the study of Banach algebras where the numerical range provides an important link between the algebraic and metric structures.
Author: F. F. Bonsall Publisher: CUP Archive ISBN: 0521079888 Category : Mathematics Languages : en Pages : 149
Book Description
The authors develop various applications, in particular to the study of Banach algebras where the numerical range provides an important link between the algebraic and metric structures.
Author: Karl E. Gustafson Publisher: Springer Science & Business Media ISBN: 1461384982 Category : Mathematics Languages : en Pages : 202
Book Description
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.
Author: Hwa-Long Gau Publisher: Cambridge University Press ISBN: 1108787606 Category : Mathematics Languages : en Pages : 556
Book Description
Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.
Author: Ulrich Daepp Publisher: American Mathematical Soc. ISBN: 147044383X Category : Conic sections Languages : en Pages : 268
Book Description
Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Whole domains of modern mathematics have arisen from exploration of such connections--consider analytic number theory or algebraic topology. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry. The book begins with Blaschke products, complex-analytic functions that are generalizations of disk automorphisms. In the analysis of Blaschke products, we encounter, in a quite natural way, an ellipse inside the unit disk. The story continues by introducing the reader to Poncelet's theorem--a beautiful result in projective geometry that ties together two conics and, in particular, two ellipses, one circumscribed by a polygon that is inscribed in the second. The Blaschke ellipse and the Poncelet ellipse turn out to be the same ellipse, and the connection is illuminated by considering the numerical range of a $2 \times 2$ matrix. The numerical range is a convex subset of the complex plane that contains information about the geometry of the transformation represented by a matrix. Through the numerical range of $n \times n$ matrices, we learn more about the interplay between Poncelet's theorem and Blaschke products. The story ranges widely over analysis, algebra, and geometry, and the exposition of the deep and surprising connections is lucid and compelling. Written for advanced undergraduates or beginning graduate students, this book would be the perfect vehicle for an invigorating and enlightening capstone exploration. The exercises and collection of extensive projects could be used as an embarkation point for a satisfying and rich research project. You are invited to read actively using the accompanying interactive website, which allows you to visualize the concepts in the book, experiment, and develop original conjectures.
Author: Panayot S Vassilevski Publisher: World Scientific ISBN: 9814531855 Category : Languages : en Pages : 925
Book Description
This volume contains the proceedings of the 4th International Conference on Numerical Methods and Applications. The major topics covered include: general finite difference, finite volume, finite element and boundary element methods, general numerical linear algebra and parallel computations, numerical methods for nonlinear problems and multiscale methods, multigrid and domain decomposition methods, CFD computations, mathematical modeling in structural mechanics, and environmental and engineering applications. The volume reflects the current research trends in the specified areas of numerical methods and their applications.
Author: Ronald Hagen Publisher: CRC Press ISBN: 1482270676 Category : Mathematics Languages : en Pages : 385
Book Description
"Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. Covers fractality and Fredholmness. Explains the phenomena of the asymptotic splitting of the singular values, and more."
Author: F. F. Bonsall
Author: F. F. Bonsall
Author: F. F. Bonsall
Author: F. F. Bonsall
Author: Karl E. Gustafson
Author: Hwa-Long Gau
Author: F. F. Bonsall
Author: Ulrich Daepp
Author: Panayot S Vassilevski
Author: Fuzhen Zhang
Author: Ronald Hagen