Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/12045

Title: Matrix equations and Hilbert's tenth problem
Authors: Bell, Paul C.
Halava, Vesa
Harju, Tero
Karhumaki, Juhani
Potapov, Igor
Keywords: Matrix equations
Formal power series
Diophantine equations
Issue Date: 2008
Publisher: © World Scientific Publishing
Citation: BELL, P.C. ... et al, 2008. Matrix equations and Hilbert's tenth problem. International Journal of Algebra and Computation, 18 (8), pp.1231-1241.
Abstract: We show a reduction of Hilbert's tenth problem to the solvability of the matrix equation Xi1 1 Xi2 2 Xik k = Z 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.
Description: Electronic version of an article published as in the International Journal of Algebra and Computation [© World Scientific Publishing Company]: http://www.worldscientific.com/doi/pdf/10.1142/S0218196708004925
Version: Accepted for publication
DOI: 10.1142/S0218196708004925
URI: https://dspace.lboro.ac.uk/2134/12045
Publisher Link: http://www.worldscientific.com/worldscinet/ijac
ISSN: 0218-1967
Appears in Collections:Published Articles (Computer Science)

Files associated with this item:

File Description SizeFormat
BelHalHarKarPotNJ.pdfAccepted version360.65 kBAdobe PDFView/Open


SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.