Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and su...Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.展开更多
Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric posit...Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.展开更多
Let F be the strong p-division ring [4]. This paper is sequel to [1]. Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned mat...Let F be the strong p-division ring [4]. This paper is sequel to [1]. Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned matrix over F is metapositive definite self-conjugate are given.Moreover,a decomposition of pairwise matrices over F with the same numbers of columns is also presented. Whence some necessary and sufficient conditions for the existence of and the explicit expression for the metapositive definite self-conjugate solution of the matrix equation AXB=C over F are derived.展开更多
文摘Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.
文摘Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.
文摘Let F be the strong p-division ring [4]. This paper is sequel to [1]. Metapositive definite self-conjugate matrix over F is defined and the necessary and sufficient conditions for determining whether a partitioned matrix over F is metapositive definite self-conjugate are given.Moreover,a decomposition of pairwise matrices over F with the same numbers of columns is also presented. Whence some necessary and sufficient conditions for the existence of and the explicit expression for the metapositive definite self-conjugate solution of the matrix equation AXB=C over F are derived.
