Paul Bell
Reachability problems in quaternion matrix and rotation semigroups
Bell, Paul
Authors
Abstract
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.
Citation
Bell, P. (2008). Reachability problems in quaternion matrix and rotation semigroups. Information and Computation, 1353 - 1361. https://doi.org/10.1016/j.ic.2008.06.004
Acceptance Date | Jun 10, 2008 |
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Publication Date | Nov 1, 2008 |
Journal | Information and Computation |
Print ISSN | 0890-5401 |
Publisher | Elsevier |
Pages | 1353 - 1361 |
DOI | https://doi.org/10.1016/j.ic.2008.06.004 |
Public URL | https://keele-repository.worktribe.com/output/423605 |
Publisher URL | https://www.sciencedirect.com/science/article/pii/S0890540108000771?via%3Dihub |
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