Geodesic
The expressions of the generalized inverses of the block tensor via the C-product
Filomat, Tome 37 (2023) no. 26, p. 8909

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DOI

In this paper, we present the expressions of the generalized inverses of the third-order 2 × 2 block tensor under the C-Product. Firstly, we give the necessary and sufficient conditions to present some generalized inverses and the Moore-Penrose inverse of the block tensor in Banachiewicz-Schur forms. Next, some results are generalized to the group inverse and the Drazin inverse. Moreover, equivalent conditions for the existence as well as the expressions for the core inverse of the block tensor are obtained. Finally, the results are applied to express the quotient property and the first Sylsvester identity of tensors.
DOI : 10.2298/FIL2326909J
Classification : 15A09, 15A24
Keywords: C-Product, block tensor, the generalized inverses, the Banachiewicz-Schur form 
Hongwei Jin; Mengyu He; Yuzhen Wang. The expressions of the generalized inverses of the block tensor via the C-product. Filomat, Tome 37 (2023) no. 26, p. 8909 . doi: 10.2298/FIL2326909J
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     title = {The expressions of the generalized inverses of the block tensor via the {C-product}},
     journal = {Filomat},
     pages = {8909 },
     year = {2023},
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     doi = {10.2298/FIL2326909J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2326909J/}
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