论文标题
关于加权矩阵几何均值的凸性不等式的注释
A Note On Convexity Inequalities Of Weighted Matrix Geometric Means
论文作者
论文摘要
我们提供了一个新的证明，以证明在正 - 半纤维矩阵的空间中使用加权矩阵几何平均值在两个点之间定义地球的非阳性曲率的鳍片歧管。使用日志大规模化技术，我们能够表明当且仅当矩阵通勤时，并且与$ \ ell^p $相同时，就会发生上述平等的平等案例。
We offer a new proof of uniform convexity inequalities for the Finsler manifold of nonpositive curvature taken on the space of positive-semidefinite matrices with the weighted matrix geometric mean defining the geodesic between two points. Using the technique of log majorization, we are able to characterize that the equality cases of said equalities occur if and only if the matrices commute, and hence are the same as in $\ell^p$.
