Reachability Problems in Quaternion Matrix and Rotation Semigroups

  • Paul Bell
  • Igor Potapov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)


We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix semigroups are undecidable in dimension two. The geometric interpretation of matrix problems over quaternions is presented in terms of rotation problems for the 2 and 3-sphere. In particular, we show that the reachability of the rotation problem is undecidable on the 3-sphere and other rotation problems can be formulated as matrix problems over complex and hypercomplex numbers.


Unit Quaternion Matrix Problem Membership Problem Reachability Problem Quaternion Matrix 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Paul Bell
    • 1
  • Igor Potapov
    • 1
  1. 1.Department of Computer Science, University of Liverpool, Ashton Building, Ashton St, Liverpool L69 3BXUK

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