# finite dimensional vector spaces second edition dover books on mathematics

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## Finite Dimensional Vector Spaces

**Author :**Paul R. Halmos

**ISBN :**9780486822266

**Genre :**Mathematics

**File Size :**78. 3 MB

**Format :**PDF, ePub

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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

**ISBN :**0691090955

**Genre :**Mathematics

**File Size :**81. 94 MB

**Format :**PDF, ePub, Docs

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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

**ISBN :**9780387900933

**Genre :**Mathematics

**File Size :**35. 21 MB

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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

## Introduction To Hilbert Space And The Theory Of Spectral Multiplicity

**Author :**Paul R. Halmos

**ISBN :**9780486826837

**Genre :**Mathematics

**File Size :**46. 11 MB

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Concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. A background in measure theory is the sole prerequisite. 1957 edition.

## Linear Algebra And Geometry

**Author :**Irving Kaplansky

**ISBN :**0486432335

**Genre :**Mathematics

**File Size :**24. 63 MB

**Format :**PDF, ePub

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The author of this text seeks to remedy a common failing in teaching algebra: the neglect of related instruction in geometry. Focusing on inner product spaces, orthogonal similarity, and elements of geometry, this volume is illustrated with an abundance of examples, exercises, and proofs and is suitable for both undergraduate and graduate courses. 1974 edition.

## Linear Algebra Problem Book

**Author :**Paul R. Halmos

**ISBN :**0883853221

**Genre :**Mathematics

**File Size :**22. 15 MB

**Format :**PDF, Mobi

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Takes the student step by step from basic axioms to advanced concepts. 164 problems, each with hints and full solutions.

## An Introduction To Linear Algebra

**Author :**L. Mirsky

**ISBN :**9780486166445

**Genre :**Mathematics

**File Size :**27. 65 MB

**Format :**PDF

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Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.

## Linear Algebra Done Right

**Author :**Sheldon Axler

**ISBN :**9783319110806

**Genre :**Mathematics

**File Size :**90. 5 MB

**Format :**PDF

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This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

## Linear Algebra Via Exterior Products

**Author :**Sergei Winitzki

**ISBN :**9781409294962

**Genre :**

**File Size :**58. 74 MB

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This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.

## Linear Algebra As An Introduction To Abstract Mathematics

**Author :**Isaiah Lankham

**ISBN :**9789814723794

**Genre :**Mathematics

**File Size :**78. 91 MB

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This is an introductory textbook designed for undergraduate mathematics majors with an emphasis on abstraction and in particular, the concept of proofs in the setting of linear algebra. Typically such a student would have taken calculus, though the only prerequisite is suitable mathematical grounding. The purpose of this book is to bridge the gap between the more conceptual and computational oriented undergraduate classes to the more abstract oriented classes. The book begins with systems of linear equations and complex numbers, then relates these to the abstract notion of linear maps on finite-dimensional vector spaces, and covers diagonalization, eigenspaces, determinants, and the Spectral Theorem. Each chapter concludes with both proof-writing and computational exercises.