Using Toeplitz matrix,the feature that the sum of the length of two sides is larger than that of the other side and the linearity transformation, the positive semi-definite sextic polynomial are derived, that is,L m(m=1,2,3,4,5),M n,B n(n=1,2,3,4) and the concrete expressions of G 1,G 2.

The author introduce the method of applying positive semi-definite quadratic form to prove inequality by giving several examples.

A sufficient and necassary condition and the general form of solutions for the inverse problem of the system of quaternion linear equations Ax=b to have solutions of positive semi-definite matrix and positive semi-definite conjugate matrix are derived.

Under the cases that the objective function is positive definite or positive semidefinite, the necessary and sufficient conditions to characterize global optimal solution are obtained.

Given two positive semidefinite matrices and their eigenvalues and a more accurate estimation of the eigenvalues of AB, we get a method of decreasing the distance between the maximum and minimum eigenvalue of AB.

It is defined for a real (may not symmetric) matrix to be generalized positive semidefinite.

This paper investigates the constraned singular semi-positive definite linear systems Ax=b,(x∈L).

In this paper,combining the majorization with compound matrix,we get an inequality for the eigenvalue of the product of positive semidefinite Hermitian matrices,which generizes some recent results.

The complex matrix solutions with Hermite part positive semidefinite and Hermite positive semidefinite for the matrix equation(A*XA,B*XB)=(C,D) is investigated.