(where is the transpose of B) has been used to characterize structured covariance matrices. For instance, the Lyapunov equations and (where A * is the conjugate transpose of A) are used to analyze of the stability of continuous-time and discrete-time systems, respectively. ![]() Linear matrix and matrix differential equations show up in various fields including engineering, mathematics, physics, statistics, control, optimization, economic, linear system and linear differential system problems. Finally, the analysis indicates that the Kronecker (Khatri-Rao) structure method can achieve good efficient while the Hadamard structure method achieve more efficient when the unknown matrices are diagonal. Second, we extend the use of connection between the Hadamard (Kronecker) product and diagonal extraction (vector) operator in order to construct a computationally-efficient solution of non-homogeneous coupled matrix differential equations that useful in various applications. ![]() First, we formulate the coupled matrix linear least-squares problem and present the efficient solutions of this problem that arises in multistatic antenna array processing problem. In the present paper, the results are organized in the following ways. To be precise about these reshaping we use the vector and diagonal extraction operators. In Kronecker products works, matrices are some times regarded as vectors and vectors are some times made in to matrices. Keywords: Matrix Products Least-Squares Problem Coupled Matrix and Matrix Differential Equations Diagonal Extraction Operator Department of Basic Sciences and Humanities, College of Engineering, University of Dammam, Dammam, KSAĮmail: Marevised Apaccepted May 4, 2012
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