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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
dc.contributor.author | Futorny, Vyacheslav |
dc.contributor.author | Klymchuk, Tetiana |
dc.contributor.author | Sergeichuk, Vladimir V. |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-03-08T16:11:39Z |
dc.date.available | 2017-03-08T16:11:39Z |
dc.date.issued | 2016-12-01 |
dc.identifier.citation | Futorny, 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.issn | 0024-3795 |
dc.identifier.uri | http://hdl.handle.net/2117/102143 |
dc.description.abstract | The 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.extent | 13 p. |
dc.language.iso | eng |
dc.publisher | Elsevier |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Equacions funcionals |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Differential equations |
dc.subject.lcsh | Matrices. |
dc.subject.other | Quaternion matrix equations |
dc.subject.other | Sylvester matrix equations |
dc.subject.other | Roth's criteria for solvability |
dc.title | 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 |
dc.type | Article |
dc.subject.lemac | Matrius (Matemàtica) |
dc.subject.lemac | Equacions diferencials |
dc.identifier.doi | 10.1016/j.laa.2016.08.022 |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0024379516303597 |
dc.rights.access | Open Access |
local.identifier.drac | 19769715 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Futorny, V.; Klymchuk, T.; Sergeichuk, V. |
local.citation.publicationName | Linear algebra and its applications |
local.citation.volume | 510 |
local.citation.startingPage | 246 |
local.citation.endingPage | 258 |
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