On invertibility and group inverse of combinations of two orthogonal projectors about a complex square matrix
Yinlan Chen · 2017
For any complex square matrix A, this paper characterizes the invertibility and group inverse of the combinations P = a1PR(A)+ a2PR(A*)+a3PR(A)PR(A*)+a4PR(A*)PR(A)by M-C-S decomposition of A. Necessary and sufficient conditions of the invertibility and its inverse are presented completely. Also, we characterize the group inverse and give an expression for P#when P is group invertible.