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

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor.author	Futorny, Vyacheslav
dc.contributor.author	Klymchuk, Tetiana
dc.contributor.author	Sergeichuk, Vladimir V.
dc.date	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.citation	0024-3795
dc.identifier.citation	10.1016/j.laa.2016.08.022
dc.identifier.uri	http://hdl.handle.net/2117/102143
dc.language.iso	eng
dc.publisher	Elsevier
dc.relation	http://www.sciencedirect.com/science/article/pii/S0024379516303597
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	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	Differential equations
dc.subject	Matrices.
dc.subject	Quaternion matrix equations
dc.subject	Sylvester matrix equations
dc.subject	Roth's criteria for solvability
dc.subject	Matrius (Matemàtica)
dc.subject	Equacions diferencials
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	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
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.

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