关于矩阵的表示及其在熵中应用

Representation of matrices and its applications to entropy

研究了矩阵酉相似概率分布表示的特性及矩阵熵凹性的应用。通过对分块矩阵、投影矩阵及矩阵熵的凹性进行研究,获得了任意方阵的酉相似概率分布的特性、任意密度矩阵关于一组完备正交投影矩阵变换的酉相似概率分布表示及矩阵熵的若干不等式。

To study the properties about the representation for probabilistic distribution of unitary similarities of a matrix and the applications about the concavity of matrix entropy, some research about block matrix, projection matrix and the concavity of matrix entropy is studied. The probabilistic distribution of unitary similarities of any square matrix, the representation of the probabilistic distribution of unitary similarities for the transformation about a complete set of orthogonal projection matrix of any density matrix and some inequalities of matrix entropy are obtained.