Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew...Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.展开更多
In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In ad...In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined.展开更多
The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a ser...The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a series of recursive relationships then we use them for constructing a novel algorithm for inverting a k-heptadiagonal matrix.The computational cost of the algorithm is calculated.Some illustrative examples are given to demonstrate the effectiveness of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China(10471085)
文摘Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.
基金Project supported by the National Natural Science Foundation of China （Grant No.60672160）
文摘In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined.
文摘The purpose of the present paper is to show a new numeric and symbolic algorithm for inverting a general nonsingular k-heptadiagonal matrix.This work is based on Doolitle LU factorization of the matrix.We obtain a series of recursive relationships then we use them for constructing a novel algorithm for inverting a k-heptadiagonal matrix.The computational cost of the algorithm is calculated.Some illustrative examples are given to demonstrate the effectiveness of the proposed method.
