Explicit tensors
نویسنده
چکیده
This is an expository article the aim of which is to introduce interested students and researchers to the topic of tensor rank, in particular to the construction of explicit tensors of high rank. We try to keep the mathematical concepts and language used as simple as possible to address a broad audience. This article is thought to be an appetizer and does not provide by any means a complete coverage of this topic. Mathematics Subject Classification (2010). 68Q17, 15A69.
منابع مشابه
An Improvement on Ranks of Explicit Tensors
We give constructions of n × n × n tensors of rank at least 2n − O(n). As a corollary we obtain an [n] shaped tensor with rank at least 2n − O(n) when r is odd. The tensors are constructed from a simple recursive pattern, and the lower bounds are proven using a partitioning theorem developed by Brockett and Dobkin. These two bounds are improvements over the previous best-known explicit tensors ...
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