Weighted Moore-Penrose inverses and fundamental theorem of even-order tensors with Einstein product

DOI10.1007/s11464-017-0628-1zbMath1393.15007OpenAlexW2588652550MaRDI QIDQ721456

Jun Ji, Yi-Min Wei

Publication date: 19 July 2018

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-017-0628-1

zbMATH Keywords

weighted Moore-Penrose inversemultilinear systemnull space and rangetensor equation

Mathematics Subject Classification ID

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

Related Items (28)

Hermitian and skew-Hermitian splitting methods for solving a tensor equation ⋮ Extension of Moore–Penrose inverse of tensor via Einstein product ⋮ Solving coupled tensor equations via higher order LSQR methods ⋮ Reverse-order law for core inverse of tensors ⋮ Conjugate gradient-like methods for solving general tensor equation with Einstein product ⋮ HOBi-CGSTAB and HOBi-CRSTAB methods for solving some tensor equations ⋮ Computation of outer inverses of tensors using the QR decomposition ⋮ Numerical range for weighted Moore-Penrose inverse of tensor ⋮ Further results on Moore-Penrose inverses of tensors with application to tensor nearness problems ⋮ SENSITIVITY OF SOME TENSOR EQUATIONS WITH EINSTEIN PRODUCT ⋮ One-sided weighted outer inverses of tensors ⋮ The Drazin inverse of an even-order tensor and its application to singular tensor equations ⋮ 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 ⋮ On reverse-order law of tensors and its application to additive results on Moore-Penrose inverse ⋮ Generalized inverses of tensors via a general product of tensors ⋮ Computing tensor generalized inverses via specialization and rationalization ⋮ Reverse-order law for weighted Moore-Penrose inverse of tensors ⋮ Numerical study on Moore-Penrose inverse of tensors via Einstein product ⋮ Reverse-order law for the Moore–Penrose inverses of tensors ⋮ Core and core-EP inverses of tensors ⋮ Developing reverse order law for the Moore-Penrose inverse with the product of three linear operators ⋮ Unnamed Item ⋮ Perturbation theory for Moore-Penrose inverse of tensor via Einstein product ⋮ Perturbation bounds for DMP and CMP inverses of tensors via Einstein product ⋮ Generalized inverses of Boolean tensors via the Einstein product ⋮ Perturbation theory for core and core-EP inverses of tensor via Einstein product

Cites Work

• Unnamed Item
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• Tensor Decompositions and Applications
• Spectra of uniform hypergraphs
• Generalized inverses. Theory and applications.
• Algebraic connectivity of an even uniform hypergraph
• Linear operators and positive semidefiniteness of symmetric tensor spaces
• Moore–Penrose inverse of tensors via Einstein product
• Solving Multilinear Systems via Tensor Inversion

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