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Filomat 2017 Volume 31, Issue 19, Pages: 6015-6019
https://doi.org/10.2298/FIL1719015M
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The DMP inverse for rectangular matrices

Meng Lingsheng (College of Mathematics and Statistics, Northwest Normal University, Lanzhou, PR China)

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.

Keywords: DMP inverse, W-weighted Drazin inverse, Moore-Penrose inverse