Multiplications and eigenvalues of tensors via linear maps

2018/09/12 by Zhaobing Fan, Chunli Deng, Haifeng Li +1 · 1 citation
Mathematics · Computer Science · #Tensor decomposition and applications #Matrix Theory and Algorithms

paper · doi:10.1080/03081087.2018.1515173

Abstract

In this paper, we study multiplications and eigenvalues of tensors by using linear maps. By the composition of linear maps, we naturally obtain two multiplications of tensors, which generalize Shao's product, Einstein product and n-mode product etc. Some properties of product of tensors are obtained directly, which don't need proofs, for example the associative law of Shao's product etc. Moreover, we extend eigenvalues of tensors to tensor representations of quivers. By using tensor representations of quivers, eigenvalues of tensors and properties are given.

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