Interpretations and Representations of Classical Tensors

2014/01/05 by Dan Jönsson, Jonsson, Dan
Computer Science · Engineering · Mathematics · #15A30 #15A69 #15A72 #46G25 #Computational Physics and Python Applications #Elasticity and Material Modeling #FOS: Mathematics #History and Overview (math.HO) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1401.0900

openalex publication_date 2014/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Classical tensors, the familiar mathematical objects denoted by symbols such as t_i, t^ij and t_k^ij, are usually interpreted either as 'coordinatizable objects' with coordinates changing in a specific way under a change of coordinate system or as elements of tensor spaces of the form V^{⊗ n}⊗(V^*)^{⊗ m}. An alternative interpretation of classical tensors as linear tensor maps of the form V^{⊗ m}→ V^{⊗ n} is presented here. In this interpretation, tensor multiplication is seen as generalized function composition. Representations of classical tensors by means of arrays are also considered.

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