Generalized tensor function via the tensor singular value decomposition based on the T-product

• Published in: Linear algebra and its applications Vol. 590; pp. 258 - 303
• Main Authors: Miao, Yun, Qi, Liqun, Wei, Yimin
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.04.2020; American Elsevier Company, Inc
• Subjects: Block tensor multiplication; Cauchy integral formula; Complex-to-real isomorphism; Cones; Decomposition; Generalized tensor function; Invariants; Isomorphism; Jordan algebra; Lie algebra; Linear algebra; Mathematical analysis; Moore-Penrose inverse; Operators (mathematics); Singular value decomposition; T-CSVD; T-product; T-SVD; Taylor series; Tensor bilinear form; Tensor-to-matrix isomorphism; Tensors; T-product; Complex-to-real isomorphism; Tensor bilinear form; T-CSVD; 15A48; 15A69; Generalized tensor function; Moore-Penrose inverse; Jordan algebra; 65F10; Cauchy integral formula; Tensor-to-matrix isomorphism; 65H10; Block tensor multiplication; Lie algebra; 65N22; T-SVD

In this paper, we present the definition of generalized tensor function according to the tensor singular value decomposition (T-SVD) based on the tensor T-product. Also, we introduce the compact singular value decomposition (T-CSVD) of tensors, from which the projection operators and Moore-Penrose i...