# Finite Dimensional Vector Spaces

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## Finite Dimensional Vector Spaces

Author | : Paul R. Halmos |

Publsiher | : Courier Dover Publications |

Total Pages | : 208 |

Release | : 2017-08-15 |

ISBN | : 0486814866 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Finite Dimensional Vector Spaces 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.

## Finite Dimensional Vector Spaces

Author | : Paul R. Halmos |

Publsiher | : Princeton University Press |

Total Pages | : 196 |

Release | : 1947-01-21 |

ISBN | : 9780691090955 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Finite Dimensional Vector Spaces 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."

## Finite Dimensional Vector Spaces

Author | : P.R. Halmos |

Publsiher | : Springer Science & Business Media |

Total Pages | : 202 |

Release | : 2012-12-06 |

ISBN | : 1461263875 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Finite Dimensional Vector Spaces 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

## Finite Dimensional Vector Spaces AM 7 Volume 7

Author | : Paul R. Halmos |

Publsiher | : Princeton University Press |

Total Pages | : 196 |

Release | : 2016-03-02 |

ISBN | : 1400882230 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Finite Dimensional Vector Spaces AM 7 Volume 7 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."

## Finite Dimensional Vector Spaces

Author | : Paul R. Halmos |

Publsiher | : Unknown |

Total Pages | : 0 |

Release | : 2022-08-20 |

ISBN | : 9781773238869 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Finite Dimensional Vector Spaces Book Excerpt:**

## Finite dimensional Vector Spaces

Author | : Paul Richard Halmos |

Publsiher | : Unknown |

Total Pages | : 199 |

Release | : 1993 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Finite dimensional Vector Spaces Book Excerpt:**

## Finite dimensional Vector Spaces

Author | : Alvin Martin Weinberg |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 1958 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Finite dimensional Vector Spaces Book Excerpt:**

## p adic Numbers

Author | : Fernando Gouvea |

Publsiher | : Springer Science & Business Media |

Total Pages | : 306 |

Release | : 2003-05-22 |

ISBN | : 9783540629115 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**p adic Numbers Book Excerpt:**

There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE

## Linear Algebra

Author | : Vivek Sahai,Vikas Bist |

Publsiher | : CRC Press |

Total Pages | : 208 |

Release | : 2002-05 |

ISBN | : 9780849324260 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Linear Algebra Book Excerpt:**

This book presents a concise, comprehensive introduction to the fundamentals of linear algebra. The authors develop the subject in a manner accessible to readers of varied backgrounds. The material requires only very basic algebra and a rudimentary knowledge of matrices and determinants as prerequisites, but the text includes an introductory chapter containing most of the foundational material required. Linear Algebra begins with the basic concepts of vector spaces, subspace, basis, and dimension. Although the authors emphasize finite dimensional vector spaces, they also include examples of infinite dimensional vector spaces to highlight the differences between the two classes. The treatment then moves to the analysis of a single linear operator on a finite dimensional vector space, including discussions on characterizing diagonizable and triangulable operators. It uses the concept of generalized eigenvectors to obtain an inductive procedure for constructing a Jordan basis for a triangulable linear operator and again uses an algorithmic approach to the rational canonical form. Subsequent discussions focus on finite dimensional inner product spaces and non-negative operators, isometries, and polar and singular-value decomposition. The final chapter explores bilinear forms and extends the results of inner product spaces to bilinear spaces. Numerous examples and exercises at the end of each section make this an outstanding text for graduate and senior undergraduate students.

## Quadratic Forms in Infinite Dimensional Vector Spaces

Author | : H. Gross |

Publsiher | : Springer Science & Business Media |

Total Pages | : 421 |

Release | : 2013-11-21 |

ISBN | : 1489935428 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Quadratic Forms in Infinite Dimensional Vector Spaces 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 (" NO-forms'''). Certain among the results 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 N-dimensional O spaces ideally serves the purpose. First, these spaces show a large number 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 NO it is easy to see, in a given case, wheth er topological language is appropriate or not).

## Finite Dimensional Linear Algebra

Author | : Mark S. Gockenbach |

Publsiher | : CRC Press |

Total Pages | : 672 |

Release | : 2010-05-06 |

ISBN | : 1439882878 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Finite Dimensional Linear Algebra 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.

## Linear Algebra

Author | : A. R. Vasishtha,J. N. Sharma |

Publsiher | : Unknown |

Total Pages | : 385 |

Release | : 1991 |

ISBN | : 1928374650XXX |

Category | : Algebrs, Linear |

Language | : EN, FR, DE, ES & NL |

**Linear Algebra Book Excerpt:**

## FINITE DIMENSIONAL VECTOR SPACES SECOND EDITION

Author | : Paul R. Halmos |

Publsiher | : Unknown |

Total Pages | : 214 |

Release | : 1958 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**FINITE DIMENSIONAL VECTOR SPACES SECOND EDITION Book Excerpt:**

## Mathematics For Bca

Author | : R.K. Rajput |

Publsiher | : Discovery Publishing House |

Total Pages | : 302 |

Release | : 2008 |

ISBN | : 9788183563369 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Mathematics For Bca Book Excerpt:**

## Berkeley Problems in Mathematics

Author | : Paulo Ney de Souza,Jorge-Nuno Silva |

Publsiher | : Springer Science & Business Media |

Total Pages | : 593 |

Release | : 2004-01-08 |

ISBN | : 9780387204291 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Berkeley Problems in Mathematics Book Excerpt:**

This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.

## Abstract Algebra with Applications

Author | : Karlheinz Spindler |

Publsiher | : CRC Press |

Total Pages | : 776 |

Release | : 1993-10-18 |

ISBN | : 9780824791445 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Abstract Algebra with Applications Book Excerpt:**

A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

## Finite Dimensional Vector Space

Author | : Billy Joe Power |

Publsiher | : Unknown |

Total Pages | : 52 |

Release | : 1960 |

ISBN | : 1928374650XXX |

Category | : Vector spaces |

Language | : EN, FR, DE, ES & NL |

**Finite Dimensional Vector Space Book Excerpt:**

## Calculus in Vector Spaces Revised Expanded

Author | : Lawrence Corwin |

Publsiher | : Routledge |

Total Pages | : 600 |

Release | : 2017-11-22 |

ISBN | : 1351462830 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Calculus in Vector Spaces Revised Expanded Book Excerpt:**

Calculus in Vector Spaces addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This second edition introduces, among other topics, the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and explains differential forms on Euclidean space, allowing for Green's theorem, Gauss's theorem, and Stokes's theorem to be understood in a natural setting. Mathematical analysts, algebraists, engineers, physicists, and students taking advanced calculus and linear algebra courses should find this book useful.

## Finite Dimensional Vector Spaces

Author | : Paul R. Halmos |

Publsiher | : Unknown |

Total Pages | : 208 |

Release | : 2013-09 |

ISBN | : 9781258809324 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Finite Dimensional Vector Spaces Book Excerpt:**

## Finite dimensional Vector Spaces

Author | : Alton Lamar Hare |

Publsiher | : Unknown |

Total Pages | : 66 |

Release | : 1961 |

ISBN | : 1928374650XXX |

Category | : Vector spaces |

Language | : EN, FR, DE, ES & NL |

**Finite dimensional Vector Spaces Book Excerpt:**