部分序上的两类矩阵优化

The two kinds of matrix majorization on the partial order

目的分析部分序上的双随机矩阵与自伴矩阵的性质。方法利用控制论方法对部分序上的双随机矩阵与自伴矩阵进行研究。结果与结论对于部分序若1≤k<n。

Objective—To analyze the properties of the stochanstic matrix and Hermitian matrix on the partial order.Methods—The majorization and spectrum theory are used to explore the structure of the stochanstic matrix and Hermitian matrix.Results and Conclusion—We will get the structure of a n n double stochanstic matrix Pif=addition,the necessary and suffii∑yi >k i∑xifor some 1≤k<n;in >k cient condition will be studied which the Hermitian matrix is a diagonal matrix.