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Numerical Range
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Book Synopsis Numerical Range by : Karl E. Gustafson
Download or read book Numerical Range written by Karl E. Gustafson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Ranges of Hilbert Space Operators by : Hwa-Long Gau
Download or read book Numerical Ranges of Hilbert Space Operators written by Hwa-Long Gau and published by Cambridge University Press. This book was released on 2021-08-05 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other by : Ulrich Daepp
Download or read book Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other written by Ulrich Daepp and published by American Mathematical Soc.. This book was released on 2018 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians delight in finding surprising connections between seemingly disparate areas of mathematics. Finding Ellipses is a delight-filled romp across a three-way unexpected connection between complex analysis, linear algebra, and projective geometry.
Book Synopsis Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras by : F. F. Bonsall
Download or read book Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras written by F. F. Bonsall and published by CUP Archive. This book was released on 1971-03-02 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Range of Holomorphic Mappings and Applications by : Mark Elin
Download or read book Numerical Range of Holomorphic Mappings and Applications written by Mark Elin and published by Springer. This book was released on 2019-03-11 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.
Book Synopsis Many-Sorted Algebras for Deep Learning and Quantum Technology by : Charles R. Giardina
Download or read book Many-Sorted Algebras for Deep Learning and Quantum Technology written by Charles R. Giardina and published by Elsevier. This book was released on 2024-02-03 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many-Sorted Algebras for Deep Learning and Quantum Technology presents a precise and rigorous description of basic concepts in Quantum technologies and how they relate to Deep Learning and Quantum Theory. Current merging of Quantum Theory and Deep Learning techniques provides a need for a text that can give readers insight into the algebraic underpinnings of these disciplines. Although analytical, topological, probabilistic, as well as geometrical concepts are employed in many of these areas, algebra exhibits the principal thread. This thread is exposed using Many-Sorted Algebras (MSA). In almost every aspect of Quantum Theory as well as Deep Learning more than one sort or type of object is involved. For instance, in Quantum areas Hilbert spaces require two sorts, while in affine spaces, three sorts are needed. Both a global level and a local level of precise specification is described using MSA. At a local level operation involving neural nets may appear to be very algebraically different than those used in Quantum systems, but at a global level they may be identical. Again, MSA is well equipped to easily detail their equivalence through text as well as visual diagrams. Among the reasons for using MSA is in illustrating this sameness. Author Charles R. Giardina includes hundreds of well-designed examples in the text to illustrate the intriguing concepts in Quantum systems. Along with these examples are numerous visual displays. In particular, the Polyadic Graph shows the types or sorts of objects used in Quantum or Deep Learning. It also illustrates all the inter and intra sort operations needed in describing algebras. In brief, it provides the closure conditions. Throughout the text, all laws or equational identities needed in specifying an algebraic structure are precisely described. - Includes hundreds of well-designed examples to illustrate the intriguing concepts in quantum systems - Provides precise description of all laws or equational identities that are needed in specifying an algebraic structure - Illustrates all the inter and intra sort operations needed in describing algebras
Book Synopsis Spectral Theory of Block Operator Matrices and Applications by : Christiane Tretter
Download or read book Spectral Theory of Block Operator Matrices and Applications written by Christiane Tretter and published by Imperial College Press. This book was released on 2008 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices. Particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not readily apply: non-self-adjoint block operator matrices, block operator matrices with unbounded entries, non-semibounded block operator matrices, and classes of block operator matrices arising in mathematical physics.The main topics include: localization of the spectrum by means of new concepts of numerical range; investigation of the essential spectrum; variational principles and eigenvalue estimates; block diagonalization and invariant subspaces; solutions of algebraic Riccati equations; applications to spectral problems from magnetohydrodynamics, fluid mechanics, and quantum mechanics.
Book Synopsis Transition And Turbulence Control by : Mohamed Gad-el-hak
Download or read book Transition And Turbulence Control written by Mohamed Gad-el-hak and published by World Scientific. This book was released on 2005-12-27 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles based on lectures given at the Workshop on Transition and Turbulence Control, hosted by the Institute for Mathematical Sciences, National University of Singapore, 8-10 December 2004. The lecturers included 13 of the world's foremost experts in the control of transitioning and turbulent flows. The chapters cover a wide range of subjects in the broad area of flow control, and will be useful to researchers working in this area in academia, government laboratories and industry. The coverage includes control theory, passive, active and reactive methods for controlling transitional and turbulent wall-bounded flows, noise suppression and mixing enhancement of supersonic turbulent jets, compliant coatings, modern flow diagnostic systems, and swept wing instabilities.
Book Synopsis Stability and Transition in Shear Flows by : Peter J. Schmid
Download or read book Stability and Transition in Shear Flows written by Peter J. Schmid and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. It presents analytical results and numerical simulations, linear and selected nonlinear stability methods. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It is equally of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Stability theory has seen a rapid development over the past decade, this book includes such new developments as direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem.
Book Synopsis Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras by : Theodore W. Palmer
Download or read book Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras written by Theodore W. Palmer and published by Cambridge University Press. This book was released on 1994-03-25 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.
Book Synopsis A Hilbert Space Problem Book by : P.R. Halmos
Download or read book A Hilbert Space Problem Book written by P.R. Halmos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."
Book Synopsis Matrix Theory: A Second Course by : James M. Ortega
Download or read book Matrix Theory: A Second Course written by James M. Ortega and published by Springer Science & Business Media. This book was released on 1987-02-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.
Book Synopsis Introduction to Linear Operator Theory by : Vasile I. Istratescu
Download or read book Introduction to Linear Operator Theory written by Vasile I. Istratescu and published by CRC Press. This book was released on 2020-08-14 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the subject and is devoted to standard material on linear functional analysis, and presents some ergodic theorems for classes of operators containing the quasi-compact operators. It discusses various classes of operators connected with the numerical range.
Book Synopsis Analysis without Borders by : Sergei Rogosin
Download or read book Analysis without Borders written by Sergei Rogosin and published by Springer Nature. This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1974-06 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Spectral Theory by : Jürgen Appell
Download or read book Nonlinear Spectral Theory written by Jürgen Appell and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: In view of the eminent importance of spectral theory of linear operators in many fields of mathematics and physics, it is not surprising that various attempts have been made to define and study spectra also for nonlinear operators. This book provides a comprehensive and self-contained treatment of the theory, methods, and applications of nonlinear spectral theory. The first chapter briefly recalls the definition and properties of the spectrum and several subspectra for bounded linear operators. Then some numerical characteristics for nonlinear operators are introduced which are useful for describing those classes of operators for which there exists a spectral theory. Since spectral values are closely related to solvability results for operator equations, various conditions for the local or global invertibility of a nonlinear operator are collected in the third chapter. The following two chapters are concerned with spectra for certain classes of continuous, Lipschitz continuous, or differentiable operators. These spectra, however, simply adapt the corresponding definitions from the linear theory which somehow restricts their applicability. Other spectra which are defined in a completely different way, but seem to have useful applications, are defined and studied in the following four chapters. The remaining three chapters are more application-oriented and deal with nonlinear eigenvalue problems, numerical ranges, and selected applications to nonlinear problems. The only prerequisite for understanding this book is a modest background in functional analysis and operator theory. It is addressed to non-specialists who want to get an idea of the development of spectral theory for nonlinear operators in the last 30 years, as well as a glimpse of the diversity of the directions in which current research is moving.
Download or read book Glasnik Matematicki written by and published by . This book was released on 1983 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
