A pair of simultaneous linear matrix equations A1XB1 = C1, A2XB2 = C2 and a matrix programming problem
TLDR
In this article, necessary and sufficient conditions are obtained for a pair of matrix equations A1XB1 = C1, A2XB2 = C2 on a general field F to have a common solution, along with the expression for a general common solution when certain conditions hold.About:
This article is published in Linear Algebra and its Applications.The article was published on 1990-04-01 and is currently open access. It has received 117 citations till now. The article focuses on the topics: Coefficient matrix & Augmented matrix.read more
Citations
More filters
Journal ArticleDOI
Ranks and the least-norm of the general solution to a system of quaternion matrix equations
Qing-Wen Wang,Cheng-Kun Li +1 more
TL;DR: Wang et al. as mentioned in this paper established a new expression of the general solution to the consistent system of linear quaternion matrix equations A1X1=C1, A2X2=C2, A3X1B1+A4X2B2 =C3.
Journal ArticleDOI
Iterative solutions to matrix equations of the form AiXBi=Fi
Jie Ding,Yanjun Liu,Feng Ding +2 more
TL;DR: For any initial value, it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values.
Journal ArticleDOI
A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
TL;DR: In this article, the classical system of matrix equations A 1 XB 1 =C 1, A 2 XB 2 =C 2 over R, an arbitrary regular ring with identity, is considered.
Journal ArticleDOI
Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems
Feng Ding,Huamin Zhang +1 more
TL;DR: By constructing an objective function and using the gradient search, a gradient-based iteration is established for solving the coupled matrix equations as mentioned in this paper, and the authors prove that the gradient solution is convergent for any initial values.
Journal ArticleDOI
The general solution to a system of real quaternion matrix equations
TL;DR: In this paper, a necessary and sufficient condition for the existence and the expression of the general solution to the system of matrix equations over real quaternion algebra @? is given.
References
More filters
Journal ArticleDOI
Generalized Inverse of Matrices and Its Applications
TL;DR: In this article, the generalized inverse of matrices and its applications are discussed and discussed in terms of generalized inverse of matrix and its application in the context of generalization of matrix matrices.
Journal ArticleDOI
Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
C. G. Khatri,Sujit Kumar Mitra +1 more
TL;DR: In this paper, necessary and sufficient conditions for existence and expressions for general Hermitian and nonnegative definite solutions are obtained for the following three systems of linear equations: (I) $AX = C, (II) $XB = D.
Journal ArticleDOI
The matrix equations AX = C, XB = D
TL;DR: For the pair of matrix equations AX = C, XB = D, the authors gives common solutions of minimum possible rank and also other feasible specified ranks and also provides a feasible specified rank.
Journal ArticleDOI
Common solutions to a pair of linear matrix equations A 1 XB 1 = C 1 and A 2 XB 2 = C 2
TL;DR: In this paper, Rao and Mitra gave a necessary and sufficient condition for the consistency of the linear matrix equation AXB = C and also its complete class of solutions, and also an expression for the general common solution.
Fixed rank solutions of linear matrix equations
TL;DR: For the matrix equation AXB=C, the authors obtained necessary and sufficient conditions for the rank of BA-C to be invariant under choice of A-C under a fixed rank.
Related Papers (5)
A representation of the general common solution to the matrix equations A1XB1 = C1 and A2XB2 = C2 with applications
Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
C. G. Khatri,Sujit Kumar Mitra +1 more