一类矩阵不等式的进一步加强

Further improvement of a class of matrix inequalities

关于Hermite矩阵A和B的v-加权几何均值的相关估计,许多学者进行了深入研究,已经获得了一系列的研究结果.利用双曲函数的性质以及双曲函数对应的泰勒展开式,得到了邹黎敏的文献中标量不等式的改进形式.再利用谱分解定理和改进后的标量不等式,改进了相应的矩阵的v-加权几何均值不等式,使之得到了进一步加强,从而改进了Kittaneh和Manasrah、邹黎敏等学者的文献中的已有结论.

Let A,B∈M_n be Hermite matrices. Many scholars have studied the v-weighted geometric mean of matrix A and B and obtained a series of results. By using Taylor’s expansion of hyperbolic function and hyperbolic function, the improved form of the winning amount inequality was obtained in Zou’s literature. Using spectral decomposition theorem and improved scalar inequality, the v-weighted geometric mean inequality of matrix was further strengthened, which are refinements of some existing inequalities obtained by Kittaneh, Manasrah, and Zou.