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Reachability problems in quaternion matrix and rotation semigroups
journal contribution
posted on 2013-04-04, 15:10 authored by Paul Bell, Igor PotapovWe 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.
History
School
- Science
Department
- Computer Science
Citation
BELL, P.C. and POTAPOV, I., 2008. Reachability problems in quaternion matrix and rotation semigroups. Information and Computation, 206 (11), pp.1353-1361.Publisher
© ElsevierVersion
- AM (Accepted Manuscript)
Publication date
2008Notes
This 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/S0890540108000771ISSN
0890-5401Publisher version
Language
- en