Waring Rank of Symmetric Tensors, and Singularities of Some Projective Hypersurfaces
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DOI: 10.1007/s00009-020-01609-0
Abstract: We show that if a homogeneous polynomial $f$ in $n$ variables has Waring rank $n+1$, then the corresponding projective hypersurface $f=0$ has at most isolated singularities, and the type of these singularities is completely determined… read more here.
Keywords: waring rank; rank; tensors singularities; symmetric tensors ... See more keywords
Computing the generalized eigenvalues of weakly symmetric tensors
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DOI: 10.1007/s10589-016-9865-6
Abstract: Tensor is a hot topic in the past decade and eigenvalue problems of higher order tensors become more and more important in the numerical multilinear algebra. Several methods for finding the Z-eigenvalues and generalized eigenvalues… read more here.
Keywords: gradient projection; method; generalized eigenvalues; weakly symmetric ... See more keywords
T-positive semidefiniteness of third-order symmetric tensors and T-semidefinite programming
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DOI: 10.1007/s10589-020-00231-w
Abstract: The T-product for third-order tensors has been used extensively in the literature. In this paper, we first introduce first-order and second-order T-derivatives for the multi-variable real-valued function with the tensor T-product. Inspired by an equivalent… read more here.
Keywords: order; third order; symmetric tensors; positive semidefiniteness ... See more keywords
Hypergraph LSS-ideals and coordinate sections of symmetric tensors
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DOI: 10.1080/00927872.2023.2196339
Abstract: Let K be a field, [n]= {1,...,n} and H=([n],E) be a hypergraph. For an integer d>= 1 the Lovasz-Saks-Schrijver ideal (LSS-ideal) L_H^K (d) in K[y_{ij}~:~(i,j) \in [n] x [d]] is the ideal generated by the… read more here.
Keywords: symmetric tensors; lss ideals; hypergraph lss; ideals coordinate ... See more keywords