Block Tensor Unfoldings
Stefan Ragnarsson, Charles F. Van Loan

TL;DR
This paper develops a concise notation and theoretical foundation for block tensor computations, including identities and the concept of block tensor unfolding, to support advanced numerical multilinear algebra algorithms.
Contribution
It introduces a new notation, proves key identities, and formalizes the notion of block tensor unfolding for improved tensor computation analysis.
Findings
Established concise notation for block tensors
Proved several useful block tensor identities
Formalized the concept of block tensor unfolding
Abstract
Within the field of numerical multilinear algebra, block tensors are increasingly important. Accordingly, it is appropriate to develop an infrastructure that supports reasoning about block tensor computation. In this paper we establish concise notation that is suitable for the analysis and development of block tensor algorithms, prove several useful block tensor identities, and make precise the notion of a block tensor unfolding.
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Taxonomy
TopicsTensor decomposition and applications · Matrix Theory and Algorithms · Model Reduction and Neural Networks
