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Exact probabilities for typical ranks of 2 × 2 × 2 and 3 × 3 × 2 tensors
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2013 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 438, no 2, 663-667 p.Article in journal (Refereed) Published
Abstract [en]

We show that the probability to be of rank 2 for a 2×2×2 tensor with elements from a standard normal distribution is π/4, and that the probability to be of rank 3 for a 3×3×2 tensor is 1/2. In the proof results on the expected number of real generalized eigenvalues of random matrices are applied. For n×n×2 tensors with n≥4 we also present some new aspects of their rank.

Place, publisher, year, edition, pages
Elsevier , 2013. Vol. 438, no 2, 663-667 p.
Keyword [en]
Tensors; Multi-way arrays; Typical rank; Random matrices
National Category
URN: urn:nbn:se:liu:diva-85549DOI: 10.1016/j.laa.2011.02.041ISI: 000313226900004OAI: diva2:571558
Available from: 2012-11-23 Created: 2012-11-23 Last updated: 2013-02-14Bibliographically approved

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Bergqvist, Göran
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Mathematics and Applied MathematicsThe Institute of Technology
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