U_x-广义正定矩阵的研究

Research on U_x-Generalized Positive Definite Matrices

正定矩阵在矩阵论中占有十分重要的地位,在实际中也有广泛的应用价值。有关广义正定矩阵已有一系列的推广。受文献[1-3]等的启发,本文进一步推广了广义正定矩阵的定义,给出了U_x-广义正定矩阵的定义,研究出了U_x-广义正定矩阵的几个充分必要条件,并得出了U_x-广义正定矩阵的判别及其若干性质,推广和改进了广义正定矩阵的一些相关研究结果。

Positive definite matrix occupies a very important position in the matrix theory, there are wide application ranges in practice. There is a series of expansion about the generalized positive definite matrix. Inspired by the literature [1- 3] and so on , this paper extends the definition of generalized positive definite matrix, the definition of Ux-generalized positive definite matrix is given in this paper,and several necessary and sufficient conditions of Ux-generalized positive definite matrix are studied.And Discrimination and some properties of Ux-generalized positive definite matrix are obtained. Some research results of the generalized positive definite matrix are generalized and improved.