Geodesic
The Sherman-Morrison-Woodbury formula for the generalized inverses
Filomat, Tome 36 (2022) no. 15, p. 5307

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DOI

In this paper, we investigate the Sherman-Morrison-Woodbury formula for the {1}-inverses and the {2}-inverses of bounded linear operators on a Hilbert space. Some conditions are established to guarantee that (A + YGZ *) ⊙ = A ⊙ − A ⊙ Y(G ⊙ + Z * A ⊙ Y) ⊙ Z * A ⊙ holds, where A ⊙ stands for any kind of standard inverse, {1}-inverse, {2}-inverse, Moore-Penrose inverse, Drazin inverse, group inverse, core inverse and dual core inverse of A.
DOI : 10.2298/FIL2215307L
Classification : 15A09, 47A05, 47A55, 46C05
Keywords: The Sherman-Morrison-Woodbury formula, {2}-inverse, {1}-inverse 
Tingting Li; Dijana Mosić; Jianlong Chen. The Sherman-Morrison-Woodbury formula for the generalized inverses. Filomat, Tome 36 (2022) no. 15, p. 5307 . doi: 10.2298/FIL2215307L
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     author = {Tingting Li and Dijana Mosi\'c and Jianlong Chen},
     title = {The {Sherman-Morrison-Woodbury} formula for the generalized inverses},
     journal = {Filomat},
     pages = {5307 },
     year = {2022},
     volume = {36},
     number = {15},
     doi = {10.2298/FIL2215307L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2215307L/}
}
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