对于A=(a_(?))∈M_n,我们知道A的行列式是一个矩阵函数,即detA=sum from α∈(?) to ε(σ) multiply from t=1 to (?) a_(to)(t)multiply from t=1 to (?) a_(to)(t)=a_(1o)(1)·a_(2o)(2)·……·a_(mo)(m)表示几个不同...对于A=(a_(?))∈M_n,我们知道A的行列式是一个矩阵函数,即detA=sum from α∈(?) to ε(σ) multiply from t=1 to (?) a_(to)(t)multiply from t=1 to (?) a_(to)(t)=a_(1o)(1)·a_(2o)(2)·……·a_(mo)(m)表示几个不同行不同列元素之积。展开更多
The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian ...The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.展开更多
文摘对于A=(a_(?))∈M_n,我们知道A的行列式是一个矩阵函数,即detA=sum from α∈(?) to ε(σ) multiply from t=1 to (?) a_(to)(t)multiply from t=1 to (?) a_(to)(t)=a_(1o)(1)·a_(2o)(2)·……·a_(mo)(m)表示几个不同行不同列元素之积。
基金The National Natural Science Foundation of China(No.11371089)the China Postdoctoral Science Foundation(No.2016M601688)
文摘The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.
