Eigenvalues of a real supersymmetric tensor

By Liqun Qi. Journal of symbolic computation, 2005

1,617 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fc59a0420364f87c2844ec68ff26af8a8ffe5b81

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In Computational Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Eigenvalues and invariants of tensors (2007, methodology): “Thus, tensors discussed in [12,14,15,19,21,25] are actually supermatrices in this paper.”
Tensor Decompositions and Applications (2009, background): “As another example, Lim [154] (see also Qi [183]) discusses higher-order extensions of singular values and eigenvalues.”
Tensor decompositions for learning latent variable models (2012, methodology): “(To simplify the discussion, we assume throughout that eigenvectors have unit norm; otherwise, for scaling reasons, we replace the above equation with T (I, u, u) = λ‖u‖u.) This concept was originally introduced in [Lim05, Qi05].”
Properties of Tensor Complementarity Problem and Some Classes of Structured Tensors (2014, background): “On the other hand, motivated by the discussion on positive definiteness of multivariate homogeneous polynomial forms [12, 13, 14], in 2005, Qi [15] introduced the concept of positive (semi-)definite symmetric tensors.”
On some properties of three different types of triangular blocked tensors (2016, neutral): “As was in [14], an order m dimension n tensor A = (ai1i2···im)1≤ij≤n (j=1,··· ,m) over the complex field C is a multidimensional array with all entries ai1i2···im ∈ C (i1, · · · , im ∈ [n] = {1, · · · , n}).”
Further results on generalized inverses of tensors via the Einstein product (2016, background): “There has been a recent surge in the research and utilization of tensors (see the articles [7, 11, 13]) which are high-order generalization of matrices.”
Some remarks on P, P0, B and B0 tensors (2014, background): “([6]) A tensor C ∈ Tm,r is called a principal sub-tensor of a tensor A = (ai1.”
Singular values and eigenvalues of tensors: a variational approach (2005, background): “A third example is the use of l-eigenvalues for order-k symmetric tensors (k even) for characterizing the positive definiteness of homogeneous polynomial forms — a problem that is important in automatic control and array signal processing (see [5, 12] and the references cited therein).”
Tensor inversion and its application to the tensor equations with Einstein product (2018, background): “Additionally, the following example reveals that the eigenvalue problem (3) is very different from those presented in [15,16].”
Spectra of Uniform Hypergraphs (2011, methodology): “We employ the following definition from [26].”