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Reachability problems in quaternion matrix and rotation semigroups
journal contributionposted on 2013-04-04, 15:10 authored by Paul Bell, Igor Potapov
We examine computational problems on quaternion matrix and ro- tation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for ma- trix 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 ro- tation problem is undecidable on the 3-sphere and other rotation problems can be formulated as matrix problems over complex and hypercomplex numbers.
- Computer Science
CitationBELL, P.C. and POTAPOV, I., 2008. Reachability problems in quaternion matrix and rotation semigroups. Information and Computation, 206 (11), pp.1353-1361.
- AM (Accepted Manuscript)
NotesThis is the author’s version of a work that was accepted for publication in the journal Information and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://www.sciencedirect.com/science/article/pii/S0890540108000771