A Generalization of the SMW Formula of OperatorA+YGZ*to the{2}-Inverse Case

摘要

The classical Sherman-Morrison-Woodbury (for short SMW) formulaA+YGZ*-1=A-1-A-1YG-1+Z*A-1Y-1Z*A-1is generalized to the{2}-inverse case. Some sufficient conditions under which the SMW formula can be represented asA+YGZ*-=A--A-YG-+Z*A-Y-Z*A-are obtained.