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• W3100352384 abstract "The equality $(mc{A}nmc{B})^dagger = mc{B}^dagger n mc{A}^dagger$ for any two complex tensors $mc{A}$ and $mc{B}$ of arbitrary order, is called as the {it reverse-order law} for the Moore-Penrose inverse of arbitrary order tensors via the Einstein product. Panigrahy {it et al.} [Linear Multilinear Algebra; 68 (2020), 246-264.] obtained several necessary and sufficient conditions to hold the reverse-order law for the Moore-Penrose inverse of even-order tensors via the Einstein product, very recently. This notion is revisited here among other results. In this context, we present several new characterizations of the reverse-order law of arbitrary order tensors via the same product. More importantly, we illustrate a result on the Moore-Penrose inverse of a sum of two tensors as an application of the reverse-order law which leaves an open problem. We recall the definition of the Frobenius norm and the spectral norm to illustrate a result for finding the additive perturbation bounds of the Moore-Penrose inverse under the Frobenius norm. We conclude our paper with the introduction of the notion of sub-proper splitting for tensors which may help to find an iterative solution of a tensor multilinear system." @default.
• W3100352384 created "2020-11-23" @default.
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• W3100352384 date "2020-08-12" @default.
• W3100352384 modified "2023-10-17" @default.
• W3100352384 title "On reverse-order law of tensors and its application to additive results on Moore–Penrose inverse" @default.
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• W3100352384 doi "https://doi.org/10.1007/s13398-020-00916-1" @default.
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