Solvability, Unique Solvability, and Representation of Solutions for Systems of Coupled Linear Matrix Equations

Authors

  • Thitison Nuchniyom Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Chalongkrung Rd., Bangkok 10520, Thailand.
  • Pattrawut Chansangiam Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Chalongkrung Rd., Bangkok 10520, Thailand.

DOI:

https://doi.org/10.26713/cma.v8i3.586

Keywords:

linear matrix equation, Kronecker product, vector operator, Moore-Penrose inverse

Abstract

We investigate a system of coupled linear matrix equations of the form AXB + CYD = E, CXD + AYB = Fwhere A,B,C,D,E,F are rectangular complex matrices and X,Y are unknown complex matrices. We obtain several criterions for solvability and unique solvability of the system and tis special cases.These criterions rely on Kronecker product, vector operator, Moore Penrose inverses, and ranks.Moreover, explicit formulas of solutions are presented.

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Published

30-12-2017
CITATION

How to Cite

Nuchniyom, T., & Chansangiam, P. (2017). Solvability, Unique Solvability, and Representation of Solutions for Systems of Coupled Linear Matrix Equations. Communications in Mathematics and Applications, 8(3), 365–378. https://doi.org/10.26713/cma.v8i3.586

Issue

Vol. 8 No. 3 (2017)

Section

Research Article

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