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Generalization of Roth's solvability criteria to systems of matrix equations

Author
Dmytryshyn, A.; Futorny, V.; Klymchuk, T.; Sergeichuk , V.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2017-08-15
Volume
527
First page
294
Last page
302
DOI
https://doi.org/10.1016/j.laa.2017.04.011 Open in new window
Repository
http://hdl.handle.net/2117/104143 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0024379517302367 Open in new window
Abstract
W.E. Roth (1952) proved that the matrix equation AX-XB=C has a solution if and only if the matrices View the MathML source and View the MathML source are similar. A. Dmytryshyn and B. Kågström (2015) extended Roth's criterion to systems of matrix equations View the MathML source(i=1,…,s) with unknown matrices X1,…,Xt, in which every Xs is X , X¿, or X¿. We extend their criterion to systems of complex matrix equations that include the complex conjugation of unknown matrices. We also prov...
Citation
Dmytryshyn, A., Futorny, V., Klymchuk, T., Sergeichuk , V. Generalization of Roth's solvability criteria to systems of matrix equations. "Linear algebra and its applications", 15 Agost 2017, vol. 527, p. 1-11.
Keywords
Roth's criteria, Sylvester equations, Systems of matrix equations
Group of research
SCL-EG - Linear Control Systems: a Geometric Approach

Participants

  • Dmytryshyn, Andrii  (author)
  • Futorny, Vyacheslav  (author)
  • Klymchuk, Tetiana  (author)
  • Sergeichuk, Vladimir V.  (author)