Extension of the GSMW Formula in Weaker Assumptions

Abstract

In this note, the generalized Sherman-Morrison-Woodbury (for short GSMW) formula ${(A+YG{Z}^{\ast })}^{\odot }=A^{\odot }-A^{\odot }Y{(G^{\odot }+Z^{\ast }{A}^{\odot }Y)}^{\odot }{Z}^{\ast }{A}^{\odot }$ is extended under some assumptions weaker than those used by Duan, 2013.