We use M<sub>n</sub> for the set of all n×n real matrices;（n）for{1,…,n};S<sub>n</sub> for the symmetricgroup on〈n〉;A[α]α∈【n〉for the principal submatrix of A determined by the ind...We use M<sub>n</sub> for the set of all n×n real matrices;（n）for{1,…,n};S<sub>n</sub> for the symmetricgroup on〈n〉;A[α]α∈【n〉for the principal submatrix of A determined by the index setα:A∈M<sub>n</sub> is called a P<sub>0</sub>（P）-matrix,if each principal minor of it is nonnegative（positive）;A∈M<sub>n</sub> is totally nonnegative if all its minors of all orders are nonnegative.It is known that if A=(α<sub>ij</sub>)∈M<sub>n</sub> is a positive semidefinite symmetric matrix,or an M-matrix or a totally nonnegative matrix,then A satisfies Fischer’s Inequality:展开更多
基金Supported partly by National Natural Science Foundation of China
文摘We use M<sub>n</sub> for the set of all n×n real matrices;（n）for{1,…,n};S<sub>n</sub> for the symmetricgroup on〈n〉;A[α]α∈【n〉for the principal submatrix of A determined by the index setα:A∈M<sub>n</sub> is called a P<sub>0</sub>（P）-matrix,if each principal minor of it is nonnegative（positive）;A∈M<sub>n</sub> is totally nonnegative if all its minors of all orders are nonnegative.It is known that if A=(α<sub>ij</sub>)∈M<sub>n</sub> is a positive semidefinite symmetric matrix,or an M-matrix or a totally nonnegative matrix,then A satisfies Fischer’s Inequality:
