【摘要】 目的　研究矩阵广义Schur补的商性质和特征值交错不等式。方法　主要利用半正定Hermi tian矩阵及矩阵Moore Penrose广义逆的性质进行研究。结果　对半正定Hermitian矩阵,给出了其广义Schur补的一个极小表示,将矩阵Schur补的商性质推广到广义Schur补,并得到几个重要不等式。结论　对半正定Hermitian矩阵,其广义Schur补具有商性质及特征值交错性质,但对一般Her mitian矩阵,这两个结果均不一定成立。更多还原

【Abstract】 AimTo study the quotient property and eigenvalues interlacing property of the generalized Schur complement.MethodsThe properties of positive semidefinite Hermitian matrices and Moore-Penrose inverse are used.ResultsA simple minimal representation,the quotient formula and several inequalities for the generalized Schur complement for positive semidefinite matrix are derived.ConclusionFor semidefinite Hermitian matrices, the quotient property and eigemalues interlacing result can be extended to the generalized Schur complement.But they do not hold for general Hermitian matrices.更多还原