Geodesic
New formulae of the Drazin inverse of anti-triangular complex block matrices
Filomat, Tome 36 (2022) no. 12, p. 4251

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DOI

Let E, F ∈ C n×n. If EF i E = 0 for all i ∈ N, we give the explicit representation of the Drazin inverse of the block complex matrix E I F 0. We thereby solve a wider kind of singular differential equations posed by Campbell [S.L. Campbell, The Drazin inverse and systems of second order linear differential equations, Linear Multilinear Algebra, 14(1983), 195–198].
DOI : 10.2298/FIL2212251C
Classification : 15A09, 65F20
Keywords: Drazin inverse, block complex matrix, singular differential equation 
Huanyin Chen; Marjan Sheibani Abdolyousefi. New formulae of the Drazin inverse of anti-triangular complex block matrices. Filomat, Tome 36 (2022) no. 12, p. 4251 . doi: 10.2298/FIL2212251C
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     title = {New formulae of the {Drazin} inverse of anti-triangular complex block matrices},
     journal = {Filomat},
     pages = {4251 },
     year = {2022},
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     doi = {10.2298/FIL2212251C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2212251C/}
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