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 : 21. 54 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.

Vector Spaces And Matrices

Author : Robert M. Thrall
ISBN : 9780486321059
Genre : Mathematics
File Size : 86. 92 MB
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Students receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. Suitable as a primary or supplementary text for college-level courses in linear algebra. 1957 edition.

Groups Matrices And Vector Spaces

Author : James B. Carrell
ISBN : 9780387794280
Genre : Mathematics
File Size : 54. 8 MB
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This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.

Linear Algebra

Author : Georgi E. Shilov
ISBN : 9780486135045
Genre : Mathematics
File Size : 49. 6 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, and more.

Algebraic Logic

Author : Paul Richard Halmos
ISBN : 0821841386
Genre : Mathematics
File Size : 34. 67 MB
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The book is a complete collection of Paul Halmos's articles written on the subject of algebraic logic (the theory of Boolean functions). Altogether, there are ten articles, which were published between 1954-1959 in eight different journals spanning four countries. The articles appear in an order that allows the reader unfamiliar with the subject to read them without many prerequisites. In particular, the first article in the book is an accessible introduction to algebraic logic.

Linear Algebra Done Right

Author : Sheldon Axler
ISBN : 9783319110806
Genre : Mathematics
File Size : 75. 35 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

Author : Walter Nef
ISBN : 0486657728
Genre : Mathematics
File Size : 32. 59 MB
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Text covers sets and mappings, vector spaces, matrices, linear functionals, other basics; plus linear programming, Tchebychev approximations, more. Ideal introduction for undergraduates; reference for theoretical, applied mathematicians. Problems and exercises.

An Introduction To Linear Algebra

Author : L. Mirsky
ISBN : 9780486166445
Genre : Mathematics
File Size : 77. 4 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.

Measure Theory

Author : Paul R. Halmos
ISBN : 9781468494402
Genre : Mathematics
File Size : 22. 83 MB
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Useful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory most useful for its application in modern analysis. Coverage includes sets and classes, measures and outer measures, Haar measure and measure and topology in groups. From the reviews: "Will serve the interested student to find his way to active and creative work in the field of Hilbert space theory." --MATHEMATICAL REVIEWS

Advanced Linear Algebra

Author : Bruce Cooperstein
ISBN : 9781439829691
Genre : Mathematics
File Size : 50. 96 MB
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Advanced Linear Algebra focuses on vector spaces and the maps between them that preserve their structure (linear transformations). It starts with familiar concepts and then slowly builds to deeper results. Along with including many exercises and examples, each section reviews what students need to know before studying the material. The book first introduces vector spaces over fields as well as the fundamental concepts of linear combinations, span of vectors, linear independence, basis, and dimension. After covering linear transformations, it discusses the algebra of polynomials with coefficients in a field, concentrating on results that are consequences of the division algorithm. The author then develops the whole structure theory of a linear operator on a finite dimensional vector space from a collection of some simple results. He also explores the entire range of topics associated with inner product spaces, from the Gram–Schmidt process to the spectral theorems for normal and self-adjoint operators on an inner product space. The text goes on to rigorously describe the trace and determinant of linear operators and square matrices. The final two chapters focus on bilinear forms and tensor products and related material. Designed for advanced undergraduate and beginning graduate students, this textbook shows students the beauty of linear algebra. It also prepares them for further study in mathematics.

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