Solvability and uniqueness criteria for generalized Sylvester-type equations Articles uri icon

publication date

  • April 2018

start page

  • 501

end page

  • 521


  • 542

International Standard Serial Number (ISSN)

  • 0024-3795

Electronic International Standard Serial Number (EISSN)

  • 1873-1856


  • We provide necessary and sufficient conditions for the generalized star-Sylvester matrix equation, AXB+(CXD)-D-star = E, to have exactly one solution for any right-hand side E. These conditions are given for arbitrary coefficient matrices A, B, C, D (either square or rectangular) and generalize existing results for the same equation with square coefficients. We also review the known results regarding the existence and uniqueness of solution for generalized Sylvester and star-Sylvester equations. (C) 2017 Elsevier Inc. All rights reserved.


  • Mathematics


  • sylvester equation; eigenvalues; matrix pencil; matrix equation