The DMP inverse for rectangular matrices

By Lingsheng Meng. 2017

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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.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/25e1e05cc7eafa7a28a831370eba4750677ef73e