Bell, PC ORCID: https://orcid.org/0000-0003-2620-635X, Halava, V, Harju, T, Karhumaki, J and Potapov, I (2008) MATRIX EQUATIONS AND HILBERT'S TENTH PROBLEM. International Journal of Algebra and Computation, 18 (8). 1231 - 1241.

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Abstract

We show a reduction of Hilbert's tenth problem to the solvability of the matrix equation over non-commuting integral matrices, where Z is the zero matrix, thus proving that the solvability of the equation is undecidable. This is in contrast to the case whereby the matrix semigroup is commutative in which the solvability of the same equation was shown to be decidable in general. The restricted problem where k = 2 for commutative matrices is known as the "A-B-C Problem" and we show that this problem is decidable even for a pair of non-commutative matrices over an algebraic number field.

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.
Uncontrolled Keywords: Matrix equations, undecidability, formal power series, diophantine equations
Subjects: Q Science > Q Science (General)
T Technology > T Technology (General)
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Depositing User: Symplectic
Date Deposited: 25 Jul 2022 10:51
Last Modified: 25 Jul 2022 10:51
URI: https://eprints.keele.ac.uk/id/eprint/11100

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