Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Matrix Groups
Download Matrix Groups full books in PDF, epub, and Kindle. Read online Matrix Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
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 250 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.
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.
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.
Book Synopsis The Random Matrix Theory of the Classical Compact Groups by : Elizabeth S. Meckes
Download or read book The Random Matrix Theory of the Classical Compact Groups written by Elizabeth S. Meckes and published by Cambridge University Press. This book was released on 2019-08-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.
Book Synopsis Lie Groups by : Harriet Suzanne Katcher Pollatsek
Download or read book Lie Groups written by Harriet Suzanne Katcher Pollatsek and published by MAA. This book was released on 2009-09-24 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a complete introduction to Lie groups for undergraduate students. The only prerequisites are multi-variable calculus and linear algebra. The emphasis is placed on the algebraic ideas, with just enough analysis to define the tangent space and the differential and to make sense of the exponential map. This textbook works on the principle that students learn best when they are actively engaged. To this end nearly 200 problems are included in the text, ranging from the routine to the challenging level. Every chapter has a section called 'Putting the pieces together' in which all definitions and results are collected for reference and further reading is suggested.
Book Synopsis The Theory of Group Characters and Matrix Representations of Groups by : Dudley Ernest Littlewood
Download or read book The Theory of Group Characters and Matrix Representations of Groups written by Dudley Ernest Littlewood and published by American Mathematical Soc.. This book was released on 2005 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally written in 1940, this book remains a classical source on representations and characters of finite and compact groups. The book starts with necessary information about matrices, algebras, and groups. Then the author proceeds to representations of finite groups. Of particular interest in this part of the book are several chapters devoted to representations and characters of symmetric groups and the closely related theory of symmetric polynomials. The concluding chapters present the representation theory of classical compact Lie groups, including a detailed description of representations of the unitary and orthogonal groups. The book, which can be read with minimal prerequisites (an undergraduate algebra course), allows the reader to get a good understanding of beautiful classical results about group representations.
Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian Hall
Download or read book Lie Groups, Lie Algebras, and Representations written by Brian Hall and published by Springer. This book was released on 2015-05-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette
Book Synopsis Matrix Inequalities and Their Extensions to Lie Groups by : Tin-Yau Tam
Download or read book Matrix Inequalities and Their Extensions to Lie Groups written by Tin-Yau Tam and published by CRC Press. This book was released on 2018-03-14 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix Inequalities and Their Extensions to Lie Groups gives a systematic and updated account of recent important extensions of classical matrix results, especially matrix inequalities, in the context of Lie groups. It is the first systematic work in the area and will appeal to linear algebraists and Lie group researchers.
Download or read book Lie Groups written by Wulf Rossmann and published by Oxford University Press, USA. This book was released on 2006 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analyzed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, root, weights and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.
Book Synopsis Structure and Geometry of Lie Groups by : Joachim Hilgert
Download or read book Structure and Geometry of Lie Groups written by Joachim Hilgert and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.
Book Synopsis Lie Groups, Lie Algebras, and Representations by : Brian C. Hall
Download or read book Lie Groups, Lie Algebras, and Representations written by Brian C. Hall and published by Springer Science & Business Media. This book was released on 2003-08-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time.
Book Synopsis Matrix Mathematics by : Dennis S. Bernstein
Download or read book Matrix Mathematics written by Dennis S. Bernstein and published by Princeton University Press. This book was released on 2009-07-26 with total page 1183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each chapter in this book describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly with cross references, citations to the literature, and illuminating remarks.
Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
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.
Book Synopsis Introduction to Affine Group Schemes by : W.C. Waterhouse
Download or read book Introduction to Affine Group Schemes written by W.C. Waterhouse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.
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.
Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd
Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
