Matrix Groups 2nd Edition Morton Curtis PB

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“Springer-Verlag; New York, 1984. Trade paperback. Second Edition. A Good, binding intact, ”... Read moreabout condition
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Condition
Good
A book that has been read but is in good condition. Very minimal damage to the cover including scuff marks, but no holes or tears. The dust jacket for hard covers may not be included. Binding has minimal wear. The majority of pages are undamaged with minimal creasing or tearing, minimal pencil underlining of text, no highlighting of text, no writing in margins. No missing pages. See all condition definitionsopens in a new window or tab
Seller Notes
“Springer-Verlag; New York, 1984. Trade paperback. Second Edition. A Good, binding intact, ...
ISBN
9780387960746
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About this product

Product Identifiers

Publisher
Springer New York
ISBN-10
0387960740
ISBN-13
9780387960746
eBay Product ID (ePID)
999983

Product Key Features

Number of Pages
Xiv, 228 Pages
Language
English
Publication Name
Matrix Groups
Subject
Algebra / Abstract, Matrices, Algebra / General
Publication Year
1984
Features
Revised
Type
Textbook
Subject Area
Mathematics
Author
M. L. Curtis
Series
Universitext Ser.
Format
Trade Paperback

Dimensions

Item Weight
25.4 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
84-014145
Dewey Edition
19
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
512/.2
Edition Description
Revised edition
Table Of Content
1 General Linear Groups.- A. Groups.- B. Fields, Quaternions.- C. Vectors and Matrices.- D. General Linear Groups.- E. Exercises.- 2 Orthogonal Groups.- A. Inner Products.- B. Orthogonal Groups.- C. The Isomorphism Question.- D. Reflections in ?n.- E. Exercises.- 3 Homomorphisms.- A. Curves in a Vector Space.- B. Smooth Homomorphisms.- C. Exercises.- 4 Exponential and Logarithm.- A. Exponential of a Matrix.- B. Logarithm.- C. One-parameter Subgroups.- D. Lie Algebras.- E. Exercises.- 5 SO(3) and Sp(1).- A. The Homomorphism ?: S3?SO(3).- B. Centers.- C. Quotient Groups.- D. Exercises.- 6 Topology.- A. Introduction.- B. Continuity of Functions, Open Sets, Closed Sets.- C. Connected Sets, Compact Sets.- D. Subspace Topology, Countable Bases.- E. Manifolds.- F. Exercises.- 7 Maximal Tori.- A. Cartesian Products of Groups.- B. Maximal Tori in Groups.- C. Centers Again.- D. Exercises.- 8 Covering by Maximal Tori.- A. General Remarks.- B. (+) for U(n) and SU(n).- C. (+) for SO(n).- D. (+) for Sp(n).- E. Reflections in ?n (again).- F. Exercises.- 9 Conjugacy of Maximal Tori.- A. Monogenic Groups.- B. Conjugacy of Maximal Tori.- C. The Isomorphism Question Again.- D. Simple Groups, Simply-Connected Groups.- E. Exercises.- 10 Spin(k).- A. Clifford Algebras.- B. Pin(k) and Spin(k).- C. The Isomorphisms.- D. Exercises.- 11 Normalizers, Weyl Groups.- A. Normalizers.- B. Weyl Groups.- C. Spin(2n+1) and Sp(n).- D. SO(n) Splits.- E. Exercises.- 12 Lie Groups.- A. Differentiable Manifolds.- B. Tangent Vectors, Vector Fields.- C. Lie Groups.- D. Connected Groups.- E. Abelian Groups.- 13.- A. Maximal Tori.- B. The Anatomy of a Reflection.- C. The Adjoint Representation.- D. Sample Computation of Roots.- Appendix 1.- Appendix 2.- References.- Supplementary Index (for Chapter 13).
Synopsis
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., 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., 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.
LC Classification Number
QA150-272

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