广义实正定矩阵的进一步研究

Further Research on General Real Positive Definite Matrix

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],[2],[3]等的启发,进一步推广了广义正定矩阵的定义,给出了全广义实正定矩阵的定义,并得出了全广义正定矩阵的几个充分必要条件及其他若干性质。推广和改进了近期广义正定矩阵的一些相关研究结果。

Positive definite matrix occupies a very important position in matrix theory, and has great value in practice. As there exist a series of expansions of these matrices, in this paper, the concept of the all general positive definte matrix is given, and some sufficient and necessary conditions of the all general positive definte matrix as well as other simple properties of this type of matrices are presented. The relevant research results of the general positive definte matrix are generalized and improved.