Eigenvalues and invariants of tensors

By Liqun Qi. 2007

273 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d1a9055e93ab43c8caa1655b722fa9e73f9f552c

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In Artificial Intelligence

In Computational Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Finding the Largest Eigenvalue of a Nonnegative Tensor (2009, background): “In recent studies of numerical multi-linear algebra [2, 3, 7, 10, 11 ], eigenvalue problems for tensors have brought special attention.”
Most Tensor Problems Are NP-Hard (2009, background): “ying other, more dicult, tensor problems. The basic notions for eigenvalues of tensors were introduced independently in [Lim 2005] and [Qi 2005], with more developments appearing in [Ni et al. 2007; Qi 2007]. Additional theory from the perspective of toric algebraic geometry and intersection theory ”
Third-Order Tensors as Operators on Matrices: A Theoretical and Computational Framework with Applications in Imaging (2013, background): “Eigenvalue decomposition for tensors means different things to different researchers (see [12] [16] [18] [19], for example).”
A new eigenvalue inclusion set for tensors and its applications (2015, background): “Recently, tensor eigenvalues and eigenvectors have received much attention in the literature [1,8,9,11,15,18–22,25].”
H$^+$-Eigenvalues of Laplacian and Signless Laplacian Tensors (2013, background): “In geometry, a tensor to a hypermatrix is like a linear transformation to a matrix - the former objects are defined without choosing bases [21].”
Conditions for Strong Ellipticity of Anisotropic Elastic Materials (2009, background): “The concept of Z-eigenvalues for tensors was introduced in [12] and further studied in [9, 13, 14].”
On the Z-eigenvalues of the adjacency tensors for uniform hypergraphs (2013, background): “Other results are based on the Z-eigenvalues or E-eigenvalues of tensors [11,15–18] of an even uniform hypergraph.”
Conditions for strong ellipticity and M-eigenvalues (2009, background): “[16], extended to a nonsymmetric case in Ref. [ 18 ], and further discussed in Refs.”
Shifted Power Method for Computing Tensor Eigenpairs (2010, background): “1 is closely related to the E-eigenpairs defined by Qi [18, 19] but differs in the constraint on x.”
Singular values of a real rectangular tensor (2010, background): “M-eigenvalues are parallel to Z-eigenvalues for square tensors [1, 3, 10, 14, 15, 16, 18].”