Matrix Groups

  • M. A. Armstrong
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The set of all invertible n × n matrices with real numbers as entries forms a group under matrix multiplication. We recall that if A = (a ij ), B = (b ij ) are two such matrices, the ijth entry of the product AB is the sum
$${a_{i1}}{b_{1j}} + {a_{i2}}{b_{2j}} + \cdot \cdot \cdot + {a_{in}}{b_{nj}}$$
Matrix multiplication is associative, the n × n identity matrix I n plays the role of identity element, and the above product AB is invertible with inverse B −l A −1.

Keywords

Matrix Multiplication Unitary Matrice Matrix Group Invertible Matrice Integer Entry 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • M. A. Armstrong
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DurhamDurhamEngland

Personalised recommendations