Matrix Groups

  • Morton L. Curtis

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Morton L. Curtis
    Pages 1-22
  3. Morton L. Curtis
    Pages 23-34
  4. Morton L. Curtis
    Pages 35-44
  5. Morton L. Curtis
    Pages 45-59
  6. Morton L. Curtis
    Pages 60-72
  7. Morton L. Curtis
    Pages 73-91
  8. Morton L. Curtis
    Pages 92-105
  9. Morton L. Curtis
    Pages 106-123
  10. Morton L. Curtis
    Pages 124-132
  11. Morton L. Curtis
    Pages 133-144
  12. Morton L. Curtis
    Pages 145-162
  13. Morton L. Curtis
    Pages 163-183
  14. Back Matter
    Pages 184-191

About this book

Introduction

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.

Keywords

Groups Matrizengruppe algebra clifford algebra field group theory homomorphism lie algebra lie group linear algebra manifold matrices matrix

Authors and affiliations

  • Morton L. Curtis
    • 1
  1. 1.Department of MathematicsRice UniversityHoustonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0093-9
  • Copyright Information Springer-Verlag New York 1979
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90462-7
  • Online ISBN 978-1-4684-0093-9
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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