Modules, Linear, and Affine Transformations

  • Guerino Mazzola
Part of the Computational Music Science book series (CMS)


Let R be a ring, then a (left) R-module is a triple (R, M, μ : R × MM) where M is an additively written abelian group and μ is the scalar multiplication, usually written as μ(r, m) = r.m if μ is clear (R is also called the ring of scalars, and M the group of vectors), with the properties:


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Guerino Mazzola
    • 1
  1. 1.School of MusicUniversity of MinnesotaMinneapolisUSA

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