Bell, PC ORCID: https://orcid.org/0000-0003-2620-635X and Potapov, I (2008) Reachability problems in quaternion matrix and rotation semigroups. Information and Computation, 206 (11). 1353 - 1361.

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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.

Item Type: Article
Additional Information: The final version of this article and all relevant information related to it, including copyrights, can be found on the publisher website.
Subjects: Q Science > QA Mathematics
T Technology > T Technology (General)
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Related URLs:
Depositing User: Symplectic
Date Deposited: 25 Jul 2022 12:27
Last Modified: 25 Jul 2022 12:27
URI: https://eprints.keele.ac.uk/id/eprint/11102

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