Geodesic
The forward order law for Moore-Penrose inverse of multiple matrix product
Filomat, Tome 37 (2023) no. 3, p. 871

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DOI

The relationship between the forward order law product A † 1 A † 2 · · · A † n of the Moore-Penrose inverses of A 1 , A 2 , · · · , A n and the seven common types of generalized inverse of A 1 A 2 · · · A n will be studied in this paper. Especially, we will give the necessary and sufficient condition for the n terms forward order law (A 1 A 2 · · · A n) † = A † 1 A † 2· · · A † n .
DOI : 10.2298/FIL2303871Z
Classification : 15A09, 15A24, 65F05
Keywords: Generalized inverse, Moore-Penrose inverse, Forward order law, Matrix product, Rank equality 
Wanna Zhou; Zhiping Xiong; Yingying Qin. The forward order law for Moore-Penrose inverse of multiple matrix product. Filomat, Tome 37 (2023) no. 3, p. 871 . doi: 10.2298/FIL2303871Z
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     title = {The forward order law for {Moore-Penrose} inverse of multiple matrix product},
     journal = {Filomat},
     pages = {871 },
     year = {2023},
     volume = {37},
     number = {3},
     doi = {10.2298/FIL2303871Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2303871Z/}
}
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