About the maximal rank of 3-tensors over the real and the complex number field

Details About the maximal rank of 3-tensors over the real and the complex number field About the maximal rank of 3-tensors over the real and the complex number field

2008-06-25

arxiv.org/abs/0806.4048v2

Ann. Inst. Stat. Math. 62, 807-822, 2010

Mathematics

Rings and Algebras

13 pages, no figure v2: correction and improvement

Scientific paper

10.1007/s10463-010-0294-5

High dimensional array data, tensor data, is becoming important in recent days. Then maximal rank of tensors is important in theory and applications. In this paper we consider the maximal rank of 3 tensors. It can be attacked from various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and Atkinson-Lloyd(1980). They treated the problem in the complex field, and we will present various bounds over the real field by proving several lemmas and propositions, which is real counterparts of their results.

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