On Third Order Tensors and Their Products

Abstract

A third order tensor is a three-way array which can be used to describe high dimensional data-set in dimensional reduction and clustering. In this paper, we mainly study the third order tensors. We introduce the slice identity tensor after the introduction of the slice product and Kronecker product defined on the set of third order tensors, and then we investigate the invertibility of the 3-order tensors in terms of the slice product. We also introduce the slice-diagonal tensors and investigate their spectrums.

Keywords

Kronecker product / slice product / slice-diagonal tensor / invertible tensor

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Peking University