The DMP inverse for rectangular matrices
Lingsheng Meng · Filomat · 2017
The definition of the DMP inverse of a square matrix with complex elements is extended to rectangular matrices by showing that for any A and W, m by n and n by m, respectively, there exists a unique matrix X, such that XAX = X, XA = Wad, wWA and (WA)k+1X =(WA)k+1A+, where Ad,w denotes the W-weighted Drazin inverse of A and k = Ind(AW), the index of AW.