COMMON LEAST-RANK SOLUTION OF MATRIX EQUATIONS A₁X₁B₁=C₁ AND A₂X₂B₂=C_{2 }WITH APPLICATIONS

Sihem Guerarra, Said Guedjiba

DOI Number
-
First page
313
Last page
323

Abstract


In this paper we will give the necessary and sufficient conditions for the paire of matrix equations A₁X₁B₁=C₁ and A₂X₂B₂=C_{2 }to have a common least-rank solution, and the expression of this solution is given, also we give the necessary and sufficient conditions for the matrix equation AXB=C to have a Hermitian least-rank solution. Using the first results, we investigate the expression of the general Hermitian least-rank solution of the matrix equation AXB=C.

Keywords


Matrix equation; Rank formulas; Moore Penrose Inverse; Hermitia; Least-rank solution.

Full Text:

PDF

References


A. Ben Israel, T. Greville, Generalized Inverse ,Theory and Applications, Kreiger, 1980.

--------------------------------------------------------------------

ca : S. L. Cambell, C. D. Meyer, Generalized Inverse of Linear Transformations, Society for industrial and applied Mathematics, 2009.

--------------------------------------------------------------------

fu : X. Fu Liu, Hu Yang, An expression of the general common least squares solution to a pair of matrix equations with applications, Comp. math. appl, 61 (2011), 3071-3078.

-----------------------------------------------------------------------

li : A. Liao, Y. Lei, Least squares solution with the minimum norm for the matrix equation (AXB,GXH)=(C,D), Comp. Math. Appl, 50 (2005), 539-549.

-------------------------------------------------------------------------

li1 : Y. Liu, Ranks of solutions of the linear matrix equation AX+YB=C, Comp. Math. Appl, 52 (2006), 861-872.

-------------------------------------------------------------------------

li2 : Y. Liu, Ranks of least squares solutions of the matrix equation AXB=C, Comp. math. appl, 55 (2008), 1270-1278.

-------------------------------------------------------------------------

mi : S. K. Mitra, A pair of of simultaneous linear matrix equations and a matrix programming problem, Linear Algebra Appl, 131 (1990), 97-123.

-------------------------------------------------------------------------

mi1 : S. K. Mitra, Common solution to a pair of linear matrix equations A₁X₁B₁=C₁ and A₂X₂B₂=C₂, Proc. Cambridge philos, Soc 74 (1973), 213-216.

-------------------------------------------------------------------------

na : A. Navarra, P. L. Odell, D. M. Yong, A representation of the general common solution A₁X₁B₁=C₁ and A₂X₂B₂=C₂ with applications, Comp. Math. Appl, 41 (2001), 929-935.

-------------------------------------------------------------------------

ti : Y. Tian, Rank Equalities Related to Generalized Inverses of Matrices and Their Applications, Master thesis, Montreal, Quebec, Canada, 2000.

-------------------------------------------------------------------------

ti1 : Y. Tian, Relations between least squares and least rank solution of the matrix equations AXB=C. Appl. math. comput, 219 (2013), 10293-10301.

-------------------------------------------------------------------------

zh : F. Zhang, Y. Li, W. Guo, J. Zhao, Least squares solutions with special structure to the linear matrix equation AXB=C, Comp. math. appl, 217 (2011), 10049-10057.


Refbacks

  • There are currently no refbacks.




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