Matrix Groups

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


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.


Matrix Multiplication Unitary Matrice Matrix Group Invertible Matrice Integer Entry 
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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

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

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