Groups Matrices And Vector Spaces

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Groups, Matrices, and Vector Spaces

Author : James B. Carrell
Publisher : Springer
ISBN 13 : 038779428X
Total Pages : 410 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Groups, Matrices, and Vector Spaces by : James B. Carrell

Download or read book Groups, Matrices, and Vector Spaces written by James B. Carrell and published by Springer. This book was released on 2017-09-02 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Algebra with Applications

Author : Karlheinz Spindler
Publisher : CRC Press
ISBN 13 : 9780824791445
Total Pages : 780 pages
Book Rating : 4.7/5 (914 download)

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Book Synopsis Abstract Algebra with Applications by : Karlheinz Spindler

Download or read book Abstract Algebra with Applications written by Karlheinz Spindler and published by CRC Press. This book was released on 1993-10-18 with total page 780 pages. Available in PDF, EPUB and Kindle. 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.

Linear Algebra and Group Theory

Author : V.I. Smirnov
Publisher : Courier Corporation
ISBN 13 : 0486265455
Total Pages : 480 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Linear Algebra and Group Theory by : V.I. Smirnov

Download or read book Linear Algebra and Group Theory written by V.I. Smirnov and published by Courier Corporation. This book was released on 2013-08-16 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derived from an encyclopedic six-volume survey, this accessible text by a prominent Soviet mathematician offers a concrete approach, with an emphasis on applications. Containing material not otherwise available to English-language readers, the three-part treatment covers determinants and systems of equations, matrix theory, and group theory. Problem sets, with hints and answers, conclude each chapter. 1961 edition.

Matrix Groups

Author : M. L. Curtis
Publisher : Springer Science & Business Media
ISBN 13 : 1461252865
Total Pages : 222 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Matrix Groups by : M. L. Curtis

Download or read book Matrix Groups written by M. L. Curtis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were developed from a course taught at Rice Univ- sity in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce students to some of the concepts of Lie group theory-- all done at the concrete level of matrix groups. As much as we could, we motivated developments as a means of deciding when two matrix groups (with different definitions) are isomorphic. In Chapter I "group" is defined and examples are given; ho- morphism and isomorphism are defined. For a field k denotes the algebra of n x n matrices over k We recall that A E Mn(k) has an inverse if and only if det A ~ 0 , and define the general linear group GL(n,k) We construct the skew-field lli of to operate linearly on llin quaternions and note that for A E Mn(lli) we must operate on the right (since we mUltiply a vector by a scalar n on the left). So we use row vectors for R , en, llin and write xA for the row vector obtained by matrix multiplication. We get a ~omplex-valued determinant function on Mn (11) such that det A ~ 0 guarantees that A has an inverse.

Matrices and Vector Spaces

Author : F. Brickell
Publisher :
ISBN 13 : 9780844809472
Total Pages : pages
Book Rating : 4.8/5 (94 download)

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Book Synopsis Matrices and Vector Spaces by : F. Brickell

Download or read book Matrices and Vector Spaces written by F. Brickell and published by . This book was released on 1972-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Vector Spaces and Matrices

Author : Robert M. Thrall
Publisher : Courier Corporation
ISBN 13 : 0486321053
Total Pages : 336 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Vector Spaces and Matrices by : Robert M. Thrall

Download or read book Vector Spaces and Matrices written by Robert M. Thrall and published by Courier Corporation. This book was released on 2014-01-15 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Vector Spaces and Matrices

Author : Robert M. Thrall
Publisher : Courier Corporation
ISBN 13 : 0486626679
Total Pages : 340 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Vector Spaces and Matrices by : Robert M. Thrall

Download or read book Vector Spaces and Matrices written by Robert M. Thrall and published by Courier Corporation. This book was released on 1970-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Algebra with Applications

Author : Karlheinz Spindler
Publisher : CRC Press
ISBN 13 : 1351469274
Total Pages : 535 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Abstract Algebra with Applications by : Karlheinz Spindler

Download or read book Abstract Algebra with Applications written by Karlheinz Spindler and published by CRC Press. This book was released on 2018-05-04 with total page 535 pages. Available in PDF, EPUB and Kindle. 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.

Matrix Groups

Author : Andrew Baker
Publisher : Springer Science & Business Media
ISBN 13 : 1447101839
Total Pages : 332 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Matrix Groups by : Andrew Baker

Download or read book Matrix Groups written by Andrew Baker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.

Mathematics For Physics: An Illustrated Handbook

Author : Adam Marsh
Publisher : World Scientific
ISBN 13 : 9813233931
Total Pages : 301 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Mathematics For Physics: An Illustrated Handbook by : Adam Marsh

Download or read book Mathematics For Physics: An Illustrated Handbook written by Adam Marsh and published by World Scientific. This book was released on 2017-11-27 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.

Linear Algebra and Matrices

Author : Shmuel Friedland
Publisher : SIAM
ISBN 13 : 1611975131
Total Pages : 301 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Linear Algebra and Matrices by : Shmuel Friedland

Download or read book Linear Algebra and Matrices written by Shmuel Friedland and published by SIAM. This book was released on 2018-01-30 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook grew out of several courses in linear algebra given over more than a decade and includes such helpful material as constructive discussions about the motivation of fundamental concepts, many worked-out problems in each chapter, and topics rarely covered in typical linear algebra textbooks.The authors use abstract notions and arguments to give the complete proof of the Jordan canonical form and, more generally, the rational canonical form of square matrices over fields. They also provide the notion of tensor products of vector spaces and linear transformations. Matrices are treated in depth, with coverage of the stability of matrix iterations, the eigenvalue properties of linear transformations in inner product spaces, singular value decomposition, and min-max characterizations of Hermitian matrices and nonnegative irreducible matrices. The authors show the many topics and tools encompassed by modern linear algebra to emphasize its relationship to other areas of mathematics. The text is intended for advanced undergraduate students. Beginning graduate students seeking an introduction to the subject will also find it of interest.

Linear Algebra as an Introduction to Abstract Mathematics

Author : Isaiah Lankham
Publisher : World Scientific Publishing Company
ISBN 13 : 9814723797
Total Pages : 208 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Linear Algebra as an Introduction to Abstract Mathematics by : Isaiah Lankham

Download or read book Linear Algebra as an Introduction to Abstract Mathematics written by Isaiah Lankham and published by World Scientific Publishing Company. This book was released on 2015-11-30 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrix Groups for Undergraduates

Author : Kristopher Tapp
Publisher : American Mathematical Soc.
ISBN 13 : 1470427222
Total Pages : 239 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Matrix Groups for Undergraduates by : Kristopher Tapp

Download or read book Matrix Groups for Undergraduates written by Kristopher Tapp and published by American Mathematical Soc.. This book was released on 2016-04-07 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots. This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups.

Matrix Groups

Author : M. L. Curtis
Publisher : Springer
ISBN 13 : 1468400932
Total Pages : 202 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Matrix Groups by : M. L. Curtis

Download or read book Matrix Groups written by M. L. Curtis and published by Springer. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were developed from a course taught at Rice Univ- sity in the spring of 1976 and again at the University of Hawaii in the spring of 1977. It is assumed that the students know some linear algebra and a little about differentiation of vector-valued functions. The idea is to introduce students to some of the concepts of Lie group theory--all done at the concrete level of matrix groups. As much as we could, we motivated developments as a means of deciding when two matrix groups (with different definitions) are isomorphie. In Chapter I "group" is defined and examples are given; ho- morphism and isomorphism are defined. For a field k denotes the algebra of n x n matrices over k We recall that A E Mn(k) has an inverse if and only if det A # 0 , and define the general linear group GL(n,k) We construct the skew-field E of quaternions and note that for A E Mn(E) to operate linearlyon Rn we must operate on the right (since we multiply a vector by a scalar n n on the left). So we use row vectors for Rn, c E and write xA , for the row vector obtained by matrix multiplication. We get a complex-valued determinant function on Mn (E) such that det A # 0 guarantees that A has an inverse.

An Introduction to Tensors and Group Theory for Physicists

Author : Nadir Jeevanjee
Publisher : Birkhäuser
ISBN 13 : 3319147943
Total Pages : 305 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis An Introduction to Tensors and Group Theory for Physicists by : Nadir Jeevanjee

Download or read book An Introduction to Tensors and Group Theory for Physicists written by Nadir Jeevanjee and published by Birkhäuser. This book was released on 2015-03-11 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques. Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups. Reviews of the First Edition “[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.” —Physics Today "Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.” —MAA Reviews

Linear Algebra and Matrix Theory

Author : Robert R. Stoll
Publisher : Courier Corporation
ISBN 13 : 0486623181
Total Pages : 290 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Linear Algebra and Matrix Theory by : Robert R. Stoll

Download or read book Linear Algebra and Matrix Theory written by Robert R. Stoll and published by Courier Corporation. This book was released on 2012-10-17 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text.

Lie Groups and Algebraic Groups

Author : Arkadij L. Onishchik
Publisher : Springer Science & Business Media
ISBN 13 : 364274334X
Total Pages : 347 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Lie Groups and Algebraic Groups by : Arkadij L. Onishchik

Download or read book Lie Groups and Algebraic Groups written by Arkadij L. Onishchik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.