Vector Spaces Of Finite Dimension

Author : Paul R. Halmos
Publisher : Princeton University Press
Page : 196 pages
File Size : 50,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882236

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Finite Dimensional Vector Spaces. (AM-7), Volume 7 by Paul R. Halmos Pdf

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 : 46,9 Mb
Release : 2017-05-24
Category : Mathematics
ISBN : 9780486822266

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Finite-Dimensional Vector Spaces by Paul R. Halmos Pdf

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 : Geoffrey Colin Shephard
Publisher : Unknown
Page : 218 pages
File Size : 54,5 Mb
Release : 1966
Category : Mathematics
ISBN : UCAL:B4486092

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Vector Spaces of Finite Dimension by Geoffrey Colin Shephard Pdf

Of set theory and algebra -- Vector spaces and subspaces -- Linear transformations -- Dual vector spaces -- Multilinear algebra -- Norms and inner products -- Coordinates and matrices.

Author : P.R. Halmos
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461263876

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Finite-Dimensional Vector Spaces by P.R. Halmos Pdf

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

Author : Paul Richard Halmos
Publisher : Unknown
Page : 0 pages
File Size : 45,6 Mb
Release : 1949
Category : Electronic
ISBN : OCLC:916118893

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Finite dimensional Vector Spaces by Paul Richard Halmos Pdf

Author : Paul R. Halmos
Publisher : Unknown
Page : 128 pages
File Size : 43,6 Mb
Release : 1942
Category : Electronic
ISBN : OCLC:1153402692

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Finite-dimensional Vector Spaces by Paul R. Halmos Pdf

Author : Herbert Gross
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 55,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475714548

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Quadratic Forms in Infinite Dimensional Vector Spaces by Herbert Gross Pdf

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) .

Author : Mark S. Gockenbach
Publisher : CRC Press
Page : 674 pages
File Size : 43,7 Mb
Release : 2011-06-15
Category : Mathematics
ISBN : 9781439815649

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Finite-Dimensional Linear Algebra by Mark S. Gockenbach Pdf

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 : Paul R. Halmos
Publisher : Unknown
Page : 208 pages
File Size : 46,8 Mb
Release : 2013-09
Category : Electronic
ISBN : 1258812584

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Finite Dimensional Vector Spaces by Paul R. Halmos Pdf

Author : Sheldon Axler
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 40,8 Mb
Release : 1997-07-18
Category : Mathematics
ISBN : 0387982590

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Linear Algebra Done Right by Sheldon Axler Pdf

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.

Author : Gottfried Köthe
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642649882

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Topological Vector Spaces I by Gottfried Köthe Pdf

It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are intro duced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces.

Author : Paul R. Halmos
Publisher : American Mathematical Soc.
Page : 333 pages
File Size : 42,9 Mb
Release : 1995-12-31
Category : Mathematics
ISBN : 9781614442127

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Linear Algebra Problem Book by Paul R. Halmos Pdf

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.

Author : Anadijiban Das
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461208938

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The Special Theory of Relativity by Anadijiban Das Pdf

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.

Author : Alex P. Robertson,Wendy Robertson
Publisher : CUP Archive
Page : 186 pages
File Size : 47,7 Mb
Release : 1980
Category : Mathematics
ISBN : 0521298822

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Topological Vector Spaces by Alex P. Robertson,Wendy Robertson Pdf

Author : Sheldon Axler
Publisher : Springer
Page : 276 pages
File Size : 55,5 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780387225951

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Linear Algebra Done Right by Sheldon Axler Pdf

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.