关于Schur-Frobenius求逆公式的一般化

On Generalization of Schur-Frobenius′s Formula for Inverse Matrix of Partitioned Matrices

中文关键词:  非交换主理想整环  von Neumann正则矩阵  广义Schur补  Schur－Frobe－nius求逆公式  Haynsworth商公式．

英文关键词:non-commutative principal ideal domain  von Neumann regular matrix  generalized Schur complement  Schur-Frobenius′s formula of inverse matrix  Haynsworth′s quotient formula.

中文摘要:

      对于（１，…，ｉ）－逆诸情形，本文证得了非交换主理想整环Ｒ上分块矩阵的Ｓｃｈｕｒ－Ｆｒｏｂｅｎｉｕｓ求逆公式的一般化定理，进而将广义Ｓｃｈｕｒ补的Ｈａｙｎｓｗｏｒｔｈ商公式开拓到Ｒ上

英文摘要:

      Let R be a non commutative principal ideal domain. A generalized theorem on Schur-Frobenius′s formula of inverse matrix in R is proved, and the Haynsworth′s quotient formula of a generalized Schur complement is generalized to R.