正定矩阵半群

Semi-groups of Positively Definite Matrices

以Pn(R)表示所有n×n实正定矩阵的集合 ,用Pn(A)表示使得AB+BA正定的n×n实矩阵B的全体 .对正定矩阵A证明了Pn(A)是Pn(R)的子半群 。

Let P n (R)be the semi group of all n by n positively definite matrices and let P n (A) be the set of all n by n real matrices such that AB+BA are positively definite.It is proved that P n (A) is a subsemigroup of the semi group P n (R),and there is a semi group isomorphism between P n (A) and P n (R).