Reverse-order law for the Moore–Penrose inverses of tensors

DOI10.1080/03081087.2018.1502252zbMath1429.15022arXiv1708.05332OpenAlexW3102912632WikidataQ114100605 ScholiaQ114100605MaRDI QIDQ5210716

Krushnachandra Panigrahy, Ratikanta Behera, Debasisha Mishra

Publication date: 21 January 2020

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05332

zbMATH Keywords

tensorMoore-Penrose inversematrixreverse-order lawEinstein product

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Multilinear algebra, tensor calculus (15A69) Applications of generalized inverses (15A10)

Related Items (18)

Hermitian and skew-Hermitian splitting methods for solving a tensor equation ⋮ Extension of Moore–Penrose inverse of tensor via Einstein product ⋮ Reverse-order law for core inverse of tensors ⋮ The Moore-Penrose inverse of tensors via the M-product ⋮ Generalized bilateral inverses of tensors via Einstein product with applications to singular tensor equations ⋮ A note on numerical ranges of tensors ⋮ HOBi-CGSTAB and HOBi-CRSTAB methods for solving some tensor equations ⋮ Further results on weighted core inverse in a ring ⋮ Numerical range for weighted Moore-Penrose inverse of tensor ⋮ Outer and (b,c) inverses of tensors ⋮ Weighted Moore-Penrose inverses of arbitrary-order tensors ⋮ A fast and efficient Newton-Shultz-type iterative method for computing inverse and Moore-Penrose inverse of tensors ⋮ Generalization of the Moore-Penrose inverse ⋮ On reverse-order law of tensors and its application to additive results on Moore-Penrose inverse ⋮ Reverse-order law for weighted Moore-Penrose inverse of tensors ⋮ Numerical study on Moore-Penrose inverse of tensors via Einstein product ⋮ Perturbation theory for Moore-Penrose inverse of tensor via Einstein product ⋮ Generalized inverses of Boolean tensors via the Einstein product

Cites Work

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• Theorems on products of \(EP_{r}\) matrices
• Moore–Penrose inverse of tensors via Einstein product
• Solving Multilinear Systems via Tensor Inversion
• Block Tensor Unfoldings
• Inverse Order Rule for Weighted Generalized Inverse
• A Jacobi-Type Method for Computing Orthogonal Tensor Decompositions
• Further results on generalized inverses of tensors via the Einstein product
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• The Pseudo-Inverse of a Product

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