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dc.contributor.authorFutorny, Vyacheslav
dc.contributor.authorKlymchuk, Tetiana
dc.contributor.authorSergeichuk, Vladimir V.
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2017-03-08T16:11:39Z
dc.date.available2017-03-08T16:11:39Z
dc.date.issued2016-12-01
dc.identifier.citationFutorny, V., Klymchuk, T., Sergeichuk , V. Roth’s solvability criteria for the matrix equations AX - XB^ = C and X - AXB^ = C over the skew field of quaternions with aninvolutive automorphism q ¿ qˆ. "Linear algebra and its applications", 1 Desembre 2016, vol. 510, p. 246-258.
dc.identifier.issn0024-3795
dc.identifier.urihttp://hdl.handle.net/2117/102143
dc.description.abstractThe matrix equation AX-XB = C has a solution if and only if the matrices A C 0 B and A 0 0 B are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988) proved that the matrix equation X - AXB = C over a field has a solution if and only if the matrices A C 0 I and I 0 0 B are simultaneously equivalent to A 0 0 I and I 0 0 B . We extend these criteria to the matrix equations AX- ^ XB = C and X - A ^ XB = C over the skew field of quaternions with a fixed involutive automorphism q ¿ ˆq.
dc.format.extent13 p.
dc.language.isoeng
dc.publisherElsevier
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Equacions funcionals
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshDifferential equations
dc.subject.lcshMatrices.
dc.subject.otherQuaternion matrix equations
dc.subject.otherSylvester matrix equations
dc.subject.otherRoth's criteria for solvability
dc.titleRoth’s solvability criteria for the matrix equations AX - XB^ = C and X - AXB^ = C over the skew field of quaternions with aninvolutive automorphism q ¿ qˆ
dc.typeArticle
dc.subject.lemacMatrius (Matemàtica)
dc.subject.lemacEquacions diferencials
dc.identifier.doi10.1016/j.laa.2016.08.022
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0024379516303597
dc.rights.accessOpen Access
local.identifier.drac19769715
dc.description.versionPostprint (author's final draft)
local.citation.authorFutorny, V.; Klymchuk, T.; Sergeichuk, V.
local.citation.publicationNameLinear algebra and its applications
local.citation.volume510
local.citation.startingPage246
local.citation.endingPage258


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