楼嫏嬛. 半正定Hermitian矩阵伪Schur补的商公式[J]. 云南大学学报(自然科学版), 2020, 42(3): 401-410. doi: 10.7540/j.ynu.20190593
引用本文: 楼嫏嬛. 半正定Hermitian矩阵伪Schur补的商公式[J]. 云南大学学报(自然科学版), 2020, 42(3): 401-410. doi: 10.7540/j.ynu.20190593
LOU Lang-huan. The quotient formulas on generalized Schur complements of positive semidefinite Hermitian matrices[J]. Journal of Yunnan University: Natural Sciences Edition, 2020, 42(3): 401-410. DOI: 10.7540/j.ynu.20190593
Citation: LOU Lang-huan. The quotient formulas on generalized Schur complements of positive semidefinite Hermitian matrices[J]. Journal of Yunnan University: Natural Sciences Edition, 2020, 42(3): 401-410. DOI: 10.7540/j.ynu.20190593

半正定Hermitian矩阵伪Schur补的商公式

The quotient formulas on generalized Schur complements of positive semidefinite Hermitian matrices

  • 摘要: 利用半正定Hermitian矩阵及其伪Schur补的性质研究半正定Hermitian矩阵伪Schur补的商性质. 通过分块矩阵的计算与比对,将矩阵Schur补的商公式推广到半正定Hermitian矩阵的伪Schur补上. 并以此为基础,得出半正定Hermitian矩阵伪Schur补的1广义逆也满足商公式以及其Moore-Penrose广义逆满足商公式的条件.

     

    Abstract: The quotient properties on generalized Schur complements of positive semidefinite Hermitian matrices are studied with the properties of positive semidefinite Hermitian matrices and their generalized Schur complements. The quotient formulas on Schur complements are extended to generalized Schur complements of positive semidefinite Hermitian matrices by computing and comparing the block matrices. Based on this, the quotient formulas on some 1 generalized inverses involving generalized Schur complements of positive semidefinite Hermitian matrices are also obtained. The condition under which the quotient formula on Moore-Penrose generalized inverse satisfies is derived.

     

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