Javad Farokhi Ostad, Mahdi Mohammadzadeh Karizaki, Mahdi Aliakbari, Amin Hosseini

DOI Number
First page
Last page


This paper is devoted to investigating some system of mixed coupled generalized Sylvester operator equations. The block operator matrix decomposition is used to find the necessary and sufficient conditions for the solvability to these systems. The solutions of the system are expressed in terms of the Moore--Penrose inverses of the coefficient operators.


Sylvester operator equations, Matrix equations, $C^*$-modules

Full Text:



Z. H. He: Pure PSVD approach to Sylvester-type quaternion matrix equations. The Electronic Journal of Linear Algebra. 35 (2019), 266-284.

Z. H. He: Some new results on a system of Sylvester-type quaternion matrix equations. Linear and Multilinear Algebra. (2019), DOI: 10.1080/03081087.2019.1704213.

Z. H. He: The General Solution to a System of Coupled Sylvester-Type Quaternion Tensor Equations Involving η- Hermicity. Bulletin of the Iranian Mathematical Society, 45(5) (2019), 1407-1430.

Z. H. He, J. Liu and T. Y. Tam: The general ϕ-Hermitian solution to mixed pairs of quaternion matrix Sylvester equations. Electron. J. Linear Algebra, 32 2017, 475-499.

Z. H. He, O. M. Agudelo, Q. W. Wang and B. De Moor: Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices. Linear Algebra and its Applications, 496 2016, 549-593.

M. Jalaeian, M. Mohammadzadeh Karizaki and M. Hassani: Conditions that the product of operators is an EP operator in Hilbert C*-module. Linear and Multilinear Algebra. 68(10) (2020), 1990-2004.

Kägström, B: A Perturbation Analysis of the Generalized Sylvester Equation (AR − LB,DR − LE) = (C, F). SIAM Journal on Matrix Analysis and Applications. 15(4) (1994), 1045–1060.

S.-G. Lee and Q.-P. Vu: Simultaneous solutions of matrix equations and simultaneous equivalence matrices. Linear Algebra Appl. 437 (2012), 2325–2339.

M. Mohammadzadeh Karizaki, D. S. Djordjevi’c, A. Hosseini and M. Jalaeian: Some results about EP modular operators. Linear and Multilinear Algebra. (2020), DOI:10.1080/03081087.2020.1844613.

M. Mohammadzadeh Karizaki, M. Hassani, M. Amyari and M. Khosravi: Operator matrix of Moore-Penrose inverse operators on Hilbert C∗-modules. Colloq. Math. 140 (2015), 171–182.

A. Shahzad , B. L. Jones , E. C. Kerrigan, G. A. Constantinides: An efficient algorithm for the solution of a coupled sylvester equation appearing in descriptor systems. Automatica. 47 (2011), 244–248.

M. Vosough and M. S. Moslehian: Solutions of the system of operator equations BXA = B = AXB = AXB via ∗-order. ELA. 32 (2017), 172-183.

Q. W. Wang, Z. H. He: Solvability conditions and general solution for the mixed Sylvester equations. Automatica. 49 (2013), 2713–2719.

Q. W. Wang, Z. H. He: Systems of coupled generalized Sylvester matrix equations. Automatica. 50 (2014) , 2840–2844.

H. K. Wimmer: Consistency of a pair of generalized Sylvester equations. IEEE Transactions on Automatic Control. 39 (1994), 1014–1016.

A. G. Wu, G. R. Duan, Y. Xue: Kronecker maps and Sylvesterpolynomial matrix equations. IEEE Transactions on Automatic Control. 52(5) (2007), 905–910.



  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)