Concrete Matrix Groups

  • Joachim HilgertEmail author
  • Karl-Hermann Neeb
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter, we mainly study the general linear group \(\mathop {\mathrm {GL}}\nolimits _{n}({\mathbb{K}})\) of invertible n×n-matrices with entries in \({\mathbb{K}}={\mathbb{R}}\) or ℂ and introduce some of its subgroups. In particular, we discuss some of the connections between matrix groups and also introduce certain symmetry groups of geometric structures like bilinear or sesquilinear forms. In Section 2.3, we introduce also groups of matrices with entries in the quaternions ℍ.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of PaderbornPaderbornGermany
  2. 2.Department of MathematicsFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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