论文标题
关于对数和不平等现象
On log-sum inequalities
论文作者
论文摘要
在信息理论中，众所周知的对数和不平等是一种基本工具，它表明相对熵的非阴性。在本文中，我们建立了一组不平等现象，这些不平等现象类似于涉及标量上定义的两个函数的对数和不等式。显示了参数扩展日志不平等。我们将这些不平等扩展到交换矩阵。此外，利用Löwner部分秩序关系和Hansen-Pedersen理论，用于非交通阳性的半明确矩阵，我们证明了许多类似于log-sum不平等的矩阵 - 质量。
In information theory, the well-known log-sum inequality is a fundamental tool which indicates the non-negativity for the relative entropy. In this article, we establish a set of inequalities which are similar to the log-sum inequality involving two functions defined on scalars. The parametric extended log-sum inequalities are shown. We extend these inequalities for the commutative matrices. In addition, utilizing the Löwner partial order relation and the Hansen-Pedersen theory for non-commutative positive semi-definite matrices we demonstrate a number of matrix-inequalities analogous to the log-sum inequality.
