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Toshio Sumi, Toshio Sakata, Mitsuhiro Miyazaki, Algebraic and Computational Aspects of Real Tensor Ranks, Springer, SpringerBriefs in Statistics, 2016.03, Recently, multi-way data or tensor data have been employed in various applied fields. We consider the decomposition of a tensor datum into a sum of rank-1 tensors, where rank-1 tensors are considered to be the simplest tensors. The minimal length of the rank-1 tensors in the sum is called the rank of the tensor. The objective of rank determination is to answer the question, “How many rank-1 tensors are required to express the given tensor?” In this book, we focus on the rank over the real number field R, which is particularly interesting for statisticians.. |