关键词: 矩阵, 特征值, 不等式

Abstract: First, two mistakes about the Minkowski inequality of [WTHX]H[WTBZ]-matrix were pointed by practical examples and reason of the mistakes was found on a view of theory analysis. On the base, some necessary conditions were improved and Minkowski inequality was further modified by considering [WTHX]H[WTBZ]-matrix properties, using eigenvalues’ distribution, inequality’s calculation and other methods，and the corresponding results were generalized. Second, another important inequality of [WTHX]H[WTBZ]-matrix was also generalized by the analysis of the Minkowski inequality. The modify and generalization not only offer supports to the [WTHX]H[WTBZ]-matrix theory itself, but also do good to development of biology, computers and mathematics and other related fields.

Key words: matrix, Eigenvalues, Inequality