Exact probabilities for typical ranks of \(2 \times 2 \times 2\) and \(3 \times 3 \times 2\) tensors
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Publication:1931760
DOI10.1016/j.laa.2011.02.041zbMath1266.15037OpenAlexW2072139290MaRDI QIDQ1931760
Publication date: 16 January 2013
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2011.02.041
Related Items (3)
Real rank boundaries and loci of forms ⋮ Systems of Polynomial Equations, Higher-Order Tensor Decompositions, and Multidimensional Harmonic Retrieval: A Unifying Framework. Part II: The Block Term Decomposition ⋮ Guarantees for Existence of a Best Canonical Polyadic Approximation of a Noisy Low-Rank Tensor
Cites Work
- Tensor Decompositions and Applications
- Symmetry transformations for square sliced three-way arrays, with applications to their typical rank
- Generic and typical ranks of multi-way arrays
- Simplicity of core arrays in three-way principal component analysis and the typical rank of \(p\times q\times 2\) arrays
- Kruskal's polynomial for \(2 \times{}2 \times{}2\) arrays and a generalization to \(2 \times{}n \times{}n\) arrays
- Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
- The probability that a random real Gaussian matrix has \(k\) real eigenvalues, related distributions, and the circular law
- Degeneracy in Candecomp/Parafac explained for \(p\times p\times 2\) arrays of rank \(p+1\) or higher
- Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
- How Many Eigenvalues of a Random Matrix are Real?
- Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
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