Please use this identifier to cite or link to this item:
https://dspace.lboro.ac.uk/2134/12044
|
| Title: | Reachability problems in quaternion matrix and rotation semigroups |
| Authors: | Bell, Paul C.
Potapov, Igor |
| Issue Date: | 2008 |
| Publisher: | © Elsevier |
| Citation: | BELL, P.C. and POTAPOV, I., 2008. Reachability problems in quaternion matrix and rotation semigroups. Information and Computation, 206 (11), pp.1353-1361. |
| Abstract: | 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. |
| Description: | 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/S0890540108000771 |
| Version: | Accepted for publication |
| DOI: | 10.1016/j.ic.2008.06.004 |
| URI: | https://dspace.lboro.ac.uk/2134/12044 |
| Publisher Link: | http://dx.doi.org/10.1016/j.ic.2008.06.004 |
| ISSN: | 0890-5401 |
| Appears in Collections: | Published Articles (Computer Science)
|
Files associated with this item:
|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
|
