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Finite Dimensional Vector Spaces
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Book Synopsis Finite Dimensional Vector Spaces. (AM-7), Volume 7 by : Paul R. Halmos
Download or read book Finite Dimensional Vector Spaces. (AM-7), Volume 7 written by Paul R. Halmos and published by Princeton University Press. This book was released on 2016-03-02 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis Finite-Dimensional Vector Spaces by : P.R. Halmos
Download or read book Finite-Dimensional Vector Spaces written by P.R. Halmos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 FÜR MATHEMATIK
Book Synopsis Finite Dimensional Vector Spaces by : Paul R. Halmos
Download or read book Finite Dimensional Vector Spaces written by Paul R. Halmos and published by Princeton University Press. This book was released on 1947-01-21 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."
Book Synopsis Linear Algebra Problem Book by : Paul R. Halmos
Download or read book Linear Algebra Problem Book written by Paul R. Halmos and published by American Mathematical Soc.. This book was released on 1995-12-31 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Finite-Dimensional Linear Algebra by : Mark S. Gockenbach
Download or read book Finite-Dimensional Linear Algebra written by Mark S. Gockenbach and published by CRC Press. This book was released on 2011-06-15 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quadratic Forms in Infinite Dimensional Vector Spaces by : Herbert Gross
Download or read book Quadratic Forms in Infinite Dimensional Vector Spaces written by Herbert Gross and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: For about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. Here we present in a systematic fashion half of the results found du ring this period, to wit, the results on denumerably infinite spaces (" ~O- forms") . Certain among the resul ts included here had of course been published at the time when they were found, others appear for the first time (the case, for example, in Chapters IX, X, XII where I in clude results contained in the Ph.D.theses by my students w. Allenspach, L. Brand, U. Schneider, M. Studer). If one wants to give an introduction to the geometric algebra of infinite dimensional quadratic spaces, a discussion of ~ -dimensional 0 spaces ideally serves the purpose. First, these spaces show a large nurober of phenomena typical of infinite dimensional spaces. Second, most proofs can be done by recursion which resembles the familiar pro cedure by induction in the finite dimensional Situation. Third, the student acquires a good feeling for the linear algebra in infinite di mensions because it is impossible to camouflage problems by topological expedients (in dimension ~O it is easy to see, in a given case, wheth er topological language is appropriate or not) .
Book Synopsis Linear Algebra Done Right by : Sheldon Axler
Download or read book Linear Algebra Done Right written by Sheldon Axler and published by Springer Science & Business Media. This book was released on 1997-07-18 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Download or read book Linear Algebra written by Paul R. Halmos and published by . This book was released on 2020-09 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, originally published as "Finite-Dimensional Vector Spaces" has been regarded as a masterpiece of linear algebra. Due to its non-standard title, the book was often overlooked even by math majors. Now the book appears with the new title, new typesetting, and corrections. The free PDF file available on the publisher's website www.bowwowpress.org
Book Synopsis Finite-Dimensional Vector Spaces by : Paul R. Halmos
Download or read book Finite-Dimensional Vector Spaces written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2017-05-24 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures in Abstract Algebra by : N. Jacobson
Download or read book Lectures in Abstract Algebra written by N. Jacobson and published by Springer. This book was released on 1975 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.
Book Synopsis The Special Theory of Relativity by : Anadijiban Das
Download or read book The Special Theory of Relativity written by Anadijiban Das and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms of the Minkowski vector space and the flat spacetime manifold. Then it discusses the kinematics of special relativity in terms of Lorentz tranformations, and treats the group structure of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of spinor (vector) space can induce a proper, orthochronous Lorentz mapping on the Minkowski vector space. The second part begins with a discussion of relativistic particle mechanics from both the Lagrangian and Hamiltonian points of view. The book then turns to the relativistic (classical) field theory, including a proof of Noether's theorem and discussions of the Klein-Gordon, electromagnetic, Dirac, and non-abelian gauge fields. The final chapter deals with recent work on classical fields in an eight-dimensional covariant phase space.
Book Synopsis Asymptotic Theory of Finite Dimensional Normed Spaces by : Vitali D. Milman
Download or read book Asymptotic Theory of Finite Dimensional Normed Spaces written by Vitali D. Milman and published by Springer. This book was released on 2009-02-27 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the geometrical structure of finite dimensional normed spaces, as the dimension grows to infinity. This is a part of what came to be known as the Local Theory of Banach Spaces (this name was derived from the fact that in its first stages, this theory dealt mainly with relating the structure of infinite dimensional Banach spaces to the structure of their lattice of finite dimensional subspaces). Our purpose in this book is to introduce the reader to some of the results, problems, and mainly methods developed in the Local Theory, in the last few years. This by no means is a complete survey of this wide area. Some of the main topics we do not discuss here are mentioned in the Notes and Remarks section. Several books appeared recently or are going to appear shortly, which cover much of the material not covered in this book. Among these are Pisier's [Pis6] where factorization theorems related to Grothendieck's theorem are extensively discussed, and Tomczak-Jaegermann's [T-Jl] where operator ideals and distances between finite dimensional normed spaces are studied in detail. Another related book is Pietch's [Pie].
Book Synopsis Finite-dimensional Vector Spaces by : Paul R. Halmos
Download or read book Finite-dimensional Vector Spaces written by Paul R. Halmos and published by . This book was released on 1942 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamentals of Linear Algebra by : J.S. Chahal
Download or read book Fundamentals of Linear Algebra written by J.S. Chahal and published by CRC Press. This book was released on 2018-12-07 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Linear Algebra is like no other book on the subject. By following a natural and unified approach to the subject it has, in less than 250 pages, achieved a more complete coverage of the subject than books with more than twice as many pages. For example, the textbooks in use in the United States prove the existence of a basis only for finite dimensional vector spaces. This book proves it for any given vector space. With his experience in algebraic geometry and commutative algebra, the author defines the dimension of a vector space as its Krull dimension. By doing so, most of the facts about bases when the dimension is finite, are trivial consequences of this definition. To name one, the replacement theorem is no longer needed. It becomes obvious that any two bases of a finite dimensional vector space contain the same number of vectors. Moreover, this definition of the dimension works equally well when the geometric objects are nonlinear. Features: Presents theories and applications in an attempt to raise expectations and outcomes The subject of linear algebra is presented over arbitrary fields Includes many non-trivial examples which address real-world problems About the Author: Dr. J.S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph.D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc, he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published a number of papers about number theory. For hobbies, he likes to travel and hike, the reason he accepted the position at Brigham Young University
Book Synopsis Finite-Dimensional Spaces by : Walter Noll
Download or read book Finite-Dimensional Spaces written by Walter Noll and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Calculus on Normed Vector Spaces by : Rodney Coleman
Download or read book Calculus on Normed Vector Spaces written by Rodney Coleman and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.
Download or read book Basic Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
