The sub-definite of matrix generalize Fischer s results on a positive definite matrix to the complex metapositive sub-definite matrix,to get a new conlusion.

In this paper,we get some necessary and sufficient conditions about the metapositive subdefinite matrix.

In this paper,we introduce the concept of metapositive subdefinite matrix over a stronger P-divisionring Ω,necessary and sufficient conditions for existence and general expression of metapositive aubdefinite solutions are obtained for the matrix equation AXB=C over

The concept of metapositive subdefinite matrix and its a series necessary and sufficient condition are given, and has reached many new results, and popularizes to one kind non-symmetric matrix on about the wellknown determinant inequality that the matrix is symmetrically positive definite Hadamard, Minkowski, Ostrowski-Taussky, Ky Fan and Openheim etc.

The definition of the extended sub metapositive definiteness matrix and n×n real matrix meta Volterra multiplicator are given.

The probrem of inegualities on the determinant of sub metapositive definiteness matrix is discussed in this paper.

On several inequalities of complex metapositive definite matrix;

The properties of metapositive definite of complex normal matrices are discussed,and a series of necessary and sufficient conditions under which of the product two complex matrices will be a complex metapositive definite matrix is given,and some new results are gained.

The concept of complex metapositive semidefinite matrix is given, its properties and determinant theories are discussed, and then the Schur theorem, Hua Luo-geng theorem, Minkowski inequality, Protruding property inequality and Ostrowski-Taussky inequality of Hermite matrices are generalized to more extensive compound matrix genus.