Matrix Groups
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Matrix Groups
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Author : M. L. Curtis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Matrix Groups written by M. L. Curtis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Matrix Representations Of Groups
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Author : Morris Newman
language : en
Publisher:
Release Date : 1968
Matrix Representations Of Groups written by Morris Newman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Matrices categories.
Matrix Groups For Undergraduates
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Author : Kristopher Tapp
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-07
Matrix Groups For Undergraduates written by Kristopher Tapp and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-07 with Compact groups categories.
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
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Author : Andrew Baker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Matrix Groups written by Andrew Baker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Matrix Groups
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Author : Dmitriĭ Alekseevich Suprunenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1976
Matrix Groups written by Dmitriĭ Alekseevich Suprunenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
This volume is a translation from the Russian of D.A. Suprunenko's book which was published in the Soviet Union in 1972. The translation was edited by K.A. Hirsch. The book gives an account of the classical results on the structure of normal subgroups of the general linear group over a division ring, of Burnside's and Schur's theorems on periodic linear groups, and of the theorem on the normal structure of SL(n, Z) for n >2. The theory of solvable, nilpotent, and locally nilpotent linear groups is also discussed.
Matrix Groups
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Author : Morton Landers Curtis
language : en
Publisher: Springer
Release Date : 1979
Matrix Groups written by Morton Landers Curtis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
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.
Matrix Groups
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Author : Dimitrij Alekseevič Suprunenko
language : en
Publisher:
Release Date : 1976
Matrix Groups written by Dimitrij Alekseevič Suprunenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
Lie Groups
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Author : Harriet Suzanne Katcher Pollatsek
language : en
Publisher: MAA
Release Date : 2009-09-24
Lie Groups written by Harriet Suzanne Katcher Pollatsek and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-24 with Mathematics categories.
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.
Matrix Groups
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Author : Morton L. Curtis
language : en
Publisher:
Release Date : 1979
Matrix Groups written by Morton L. Curtis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Matrix groups categories.
These notes were developed from a course taught at Rice University 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 some students to some of the concepts of Lie group theory --all done at the concrete level of matrix groups.
The Theory Of Group Characters And Matrix Representations Of Groups
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Author : Dudley Ernest Littlewood
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
The Theory Of Group Characters And Matrix Representations Of Groups written by Dudley Ernest Littlewood and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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.