Interpretations and Representations of Classical Tensors

Por • 16 ene, 2014 • Sección: Ciencia y tecnología

Dan Jonsson

Abstract: Classical tensors, the familiar mathematical objects denoted by symbols such as t i   , t ij   and t ij k   , 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.

arXiv:1401.0900v1 [math.HO]

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