Download Full eBooks in PDF
Finite Dimensional Linear Analysis Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Finite Dimensional Linear Analysis book. This book definitely worth reading, it is an incredibly well-written.
Author : I. M. Glazman
Publisher : Courier Corporation
Page : 548 pages
File Size : 48,7 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9780486453323
A sequence of 2,400 propositions and problems features only hints. Suitable for advanced undergraduates and graduate students, this unique approach encourages students to work out their own proofs. 1974 edition.
Author : Израиль Маркович Глазман,I͡Uriĭ Ilʹich Li͡ubich
Publisher : MIT Press (MA)
Page : 520 pages
File Size : 49,8 Mb
Release : 1974
Category : Algebras, Linear
ISBN : 0262070588
First published in Russian in 1969, this remarkable book develops the subject of linear algebra in a novel fashion: it presents a logically interconnected sequence of propositions and problems--some 2400 in all--"without proofs" but with a scaffolding of hints and pointers. The student is asked to work out formal proofs systematically, proceeding from simple verifications to relatively advanced strategies and techniques of proof. The material is organized into ten chapters.The authors have based their approach on the fundamental pedagogic proposition that the best way to learn mathematics is to "do" mathematics-- that the essence of understanding any given set of mathematical propositions comes when the student succeeds in proving them for himself, however roughly, rather than after a mere reading of a series of proofs, however polished. This aspect of the book will appeal to strongly motivated students: it can be used as a resource for independent study and in cooperative seminars, preferably without faculty presence. Of course, it can also be used as the basis of more conventional lecture presentations. It is suggested that the book be introduced at the senior or the first-year graduate level.The book is also meant to give insight into functional analysis, which may be formulated as linear analysis within an infinite-dimensional framework. As the student allows his consideration of the propositions move toward the limiting case of unrestricted dimensionality, he will find that his conceptual outlook approaches that proper to functional analysis. In that regard, the book represents an introduction to the latter subject, free of the difficulties inherent in the explicit admission of infinities.
Author : Mark S. Gockenbach
Publisher : CRC Press
Page : 674 pages
File Size : 43,9 Mb
Release : 2011-06-15
Category : Mathematics
ISBN : 9781439815649
Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation. The author begins with an overview of the essential themes of the book: linear equations, best approximation, and diagonalization. He then takes students through an axiomatic development of vector spaces, linear operators, eigenvalues, norms, and inner products. In addition to discussing the special properties of symmetric matrices, he covers the Jordan canonical form, an important theoretical tool, and the singular value decomposition, a powerful tool for computation. The final chapters present introductions to numerical linear algebra and analysis in vector spaces, including a brief introduction to functional analysis (infinite-dimensional linear algebra). Drawing on material from the author’s own course, this textbook gives students a strong theoretical understanding of linear algebra. It offers many illustrations of how linear algebra is used throughout mathematics.
Author : Roger W. Brockett
Publisher : SIAM
Page : 260 pages
File Size : 44,9 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9781611973877
Originally published in 1970, Finite Dimensional Linear Systems is a classic textbook that provides a solid foundation for learning about dynamical systems and encourages students to develop a reliable intuition for problem solving. The theory of linear systems has been the bedrock of control theory for 50 years and has served as the springboard for many significant developments, all the while remaining impervious to change. Since linearity lies at the heart of much of the mathematical analysis used in applications, a firm grounding in its central ideas is essential. This book touches upon many of the standard topics in applied mathematics, develops the theory of linear systems in a systematic way, making as much use as possible of vector ideas, and contains a number of nontrivial examples and many exercises.
Author : Paul R. Halmos
Publisher : Princeton University Press
Page : 196 pages
File Size : 43,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882236
As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938--even though he did not have a fellowship--to study among the many giants of mathematics who had recently joined the faculty. He eventually became John von Neumann's research assistant, and it was one of von Neumann's inspiring lectures that spurred Halmos to write Finite Dimensional Vector Spaces. The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic flow, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space."
Author : Paul R. Halmos
Publisher : Courier Dover Publications
Page : 208 pages
File Size : 50,7 Mb
Release : 2017-05-24
Category : Mathematics
ISBN : 9780486822266
Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.
Author : Charalambos D. Aliprantis,Kim C. Border
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 52,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662039618
This book presents functional analytic methods in a unified manner with applications to economics, social sciences, and engineering. Ideal for those without an extensive background in the area, it develops topology, convexity, Banach lattices, integration, correspondences, and the analytic approach to Markov processes. Many of the results were previously available only in esoteric monographs and will interest researchers and students who will find the material readily applicable to problems in control theory and economics.
Author : Bryan Rynne,M.A. Youngson
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 49,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781447136552
This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
Author : Paul R Halmos
Publisher : Unknown
Page : 0 pages
File Size : 54,9 Mb
Release : 2022-08-20
Category : Electronic
ISBN : 1773238868
Master expositor Paul Halmos presents Linear Algebra in the pure axiomatic spirit. He writes "My purpose in this book is to treat linear transformations on finite dimensional vector spaces by the methods of more general theories. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications, and to do so in a language that gives away the trade secrets ...". This text is an ideal supplement to modern treatments of Linear Algebra. "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity....The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." --Zentralblatt für Mathematik.
Author : Michael I. Gil'
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 52,7 Mb
Release : 1998-09-30
Category : Mathematics
ISBN : 0792382218
The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations. Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint. This book contains solutions to the problems connected with the Aizerman and generalized Aizerman conjectures and presents fundamental results by A. Yu. Levin for the stability of nonautonomous systems having variable real characteristic roots. Stability of Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first-year graduate-level course in analysis.
Author : Roger W. Brockett
Publisher : SIAM
Page : 260 pages
File Size : 54,7 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9781611973884
Originally published in 1970, Finite Dimensional Linear Systems is a classic textbook that provides a solid foundation for learning about dynamical systems and encourages students to develop a reliable intuition for problem solving. The theory of linear systems has been the bedrock of control theory for 50 years and has served as the springboard for many significant developments, all the while remaining impervious to change. Since linearity lies at the heart of much of the mathematical analysis used in applications, a firm grounding in its central ideas is essential. This book touches upon many of the standard topics in applied mathematics, develops the theory of linear systems in a systematic way, making as much use as possible of vector ideas, and contains a number of nontrivial examples and many exercises.
Author : P R Halmos
Publisher : Unknown
Page : 212 pages
File Size : 42,8 Mb
Release : 1974-01-01
Category : Espacios vectoriales
ISBN : 1461263883
From the reviews: "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity....The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." --ZENTRALBLATT FUR MATHEMATIK
Author : Ruth F. Curtain,Hans Zwart
Publisher : Springer Science & Business Media
Page : 714 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242246
Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook for a course on infinite dimensional linear systems. An important consideration by the authors is that their book should be accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Consequently, all the mathematical background is summarized in an extensive appendix. For the majority of students, this would be their only acquaintance with infinite dimensional systems.
Author : Walter Noll
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401093354
A. Audience. This treatise (consisting of the present VoU and of VoUI, to be published) is primarily intended to be a textbook for a core course in mathematics at the advanced undergraduate or the beginning graduate level. The treatise should also be useful as a textbook for selected stu dents in honors programs at the sophomore and junior level. Finally, it should be of use to theoretically inclined scientists and engineers who wish to gain a better understanding of those parts of mathemat ics that are most likely to help them gain insight into the conceptual foundations of the scientific discipline of their interest. B. Prerequisites. Before studying this treatise, a student should be familiar with the material summarized in Chapters 0 and 1 of Vol.1. Three one-semester courses in serious mathematics should be sufficient to gain such fa miliarity. The first should be an introduction to contemporary math ematics and should cover sets, families, mappings, relations, number systems, and basic algebraic structures. The second should be an in troduction to rigorous real analysis, dealing with real numbers and real sequences, and with limits, continuity, differentiation, and integration of real functions of one real variable. The third should be an intro duction to linear algebra, with emphasis on concepts rather than on computational procedures. C. Organization.
Author : Paul R. Halmos
Publisher : American Mathematical Soc.
Page : 333 pages
File Size : 41,6 Mb
Release : 1995-12-31
Category : Mathematics
ISBN : 9781614442127
Linear Algebra Problem Book can be either the main course or the dessert for someone who needs linear algebraand today that means every user of mathematics. It can be used as the basis of either an official course or a program of private study. If used as a course, the book can stand by itself, or if so desired, it can be stirred in with a standard linear algebra course as the seasoning that provides the interest, the challenge, and the motivation that is needed by experienced scholars as much as by beginning students. The best way to learn is to do, and the purpose of this book is to get the reader to DO linear algebra. The approach is Socratic: first ask a question, then give a hint (if necessary), then, finally, for security and completeness, provide the detailed answer.
