论文标题
Brunn-Minkovski不平等到多个矩阵的扩展
Extensions of Brunn-Minkovski's inequality to multiple matrices
论文作者
论文摘要
Yuan and Leng（2007）对Ky Fan的决定性不平等进行了概括，这是Brunn-Minkowski的基本著名的改进半限定矩阵。在本说明中，我们首先将Yuan-Leng的结果扩展到多个正定矩阵，然后将结果进一步扩展到较大类别的矩阵，其数值范围包含在一个扇区中。我们的结果改善了LIU的最新结果[线性代数应用。 508（2016）206--213]。
Yuan and Leng (2007) gave a generalization of Ky Fan's determinantal inequality, which is a celebrated refinement of the fundamental Brunn-Minkowski inequality $(\det (A+B))^{1/n} \ge (\det A)^{1/n} +(\det B)^{1/n}$, where $A$ and $B$ are positive semidefinite matrices. In this note, we first give an extension of Yuan-Leng's result to multiple positive definite matrices, and then we further extend the result to a larger class of matrices whose numerical ranges are contained in a sector. Our result improves a recent result of Liu [Linear Algebra Appl. 508 (2016) 206--213].
