In this paper, not only the definition of the line semi-positive definite matrix and thegeneralized line semi-positive definite matrix were proposed, but also their relative properties,determine conditions, the generalization of the line semi-positive definition matrix. And somenew conclusions were obtained such as real matrix is the number of necessary and sufficientconditions of the line semi-positive definite matrix, the determine conditions of thegeneralization of line semi-positive definite matrix, the determinant inequality of the linesemi-positive definite matrix and so on. |