Exact probabilities for typical ranks of 2 × 2 × 2 and 3 × 3 × 2 tensors
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
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.
Tensors; Multi-way arrays; Typical rank; Random matrices
IdentifiersURN: urn:nbn:se:liu:diva-85549DOI: 10.1016/j.laa.2011.02.041ISI: 000313226900004OAI: oai:DiVA.org:liu-85549DiVA: diva2:571558