an introduction to the theory of linear spaces dover books on mathematics

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An Introduction To The Theory Of Linear Spaces

Author : Georgi E. Shilov
ISBN : 9780486139432
Genre : Mathematics
File Size : 30. 42 MB
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Introductory treatment offers a clear exposition of algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. Numerous examples illustrate many different fields, and problems include hints or answers. 1961 edition.

Linear Algebra

Author : Georgi? Evgen?evich Shilov
ISBN : 048663518X
Genre : Mathematics
File Size : 29. 68 MB
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Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Topological Vector Spaces And Distributions

Author : John Horvath
ISBN : 9780486311036
Genre : Mathematics
File Size : 64. 33 MB
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"The most readable introduction to the theory of vector spaces available in English and possibly any other language."—J. L. B. Cooper, MathSciNet Review Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers. The precise exposition of the first three chapters—covering Banach spaces, locally convex spaces, and duality—provides an excellent summary of the modern theory of locally convex spaces. The fourth and final chapter develops the theory of distributions in relation to convolutions, tensor products, and Fourier transforms. Augmented with many examples and exercises, the text includes an extensive bibliography.

Theory Of Linear Operators In Hilbert Space

Author : N. I. Akhiezer
ISBN : 9780486318653
Genre : Mathematics
File Size : 42. 80 MB
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This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.

An Introduction To Linear Algebra

Author : L. Mirsky
ISBN : 9780486166445
Genre : Mathematics
File Size : 69. 3 MB
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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.

Theory Of Linear Operations

Author : S. Banach
ISBN : 0080887201
Genre : Mathematics
File Size : 74. 57 MB
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This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra. The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series. A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.

Introduction To Spectral Theory In Hilbert Space

Author : Gilbert Helmberg
ISBN : 9780486466224
Genre : Mathematics
File Size : 83. 68 MB
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This text introduces students to Hilbert space and bounded self-adjoint operators, as well as the spectrum of an operator and its spectral decomposition. The author, Emeritus Professor of Mathematics at the University of Innsbruck, Austria, has ensured that the treatment is accessible to readers with no further background than a familiarity with analysis and analytic geometry. Starting with a definition of Hilbert space and its geometry, the text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators. Extensive appendixes offer supplemental information on the graph of a linear operator and the Riemann-Stieltjes and Lebesgue integration.

Elementary Functional Analysis

Author : Georgi E. Shilov
ISBN : 9780486318684
Genre : Mathematics
File Size : 38. 36 MB
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Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.

Finite Dimensional Vector Spaces

Author : Paul R. Halmos
ISBN : 9780486822266
Genre : Mathematics
File Size : 45. 88 MB
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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.

A Vector Space Approach To Geometry

Author : Melvin Hausner
ISBN : 9780486137858
Genre : Mathematics
File Size : 52. 42 MB
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This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965 edition.

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