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General Linear Groups

  • Morton L. Curtis
Part of the Universitext book series (UTX)

Abstract

Before we can discuss matrix groups we need to talk a little about groups in general. If X and Y are sets, their Cartesian product X × Y is defined to be the set of all ordered pairs (x,y) with x ∈ X and y ∈ Y. A convenient notation for describing this set of all ordered pairs is
$$X + Y = \left\{ {\left( {x,y} \right)|x \in X\;and\;y \in Y} \right\},$$
the curly brackets being read as “the set of all” and the vertical bar as “such that.”

Keywords

Vector Space Positive Real Number Binary Operation Identity Element Multiplicative Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

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

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