Tensor: Difference between revisions

Revision as of 11:35, 13 July 2025

Latest revision as of 13:06, 15 July 2025

(2 intermediate revisions by the same user not shown)

Line 389:

===Machine learning===

{{Main|Tensor (machine learning)}}

The properties of tensors, especially [[tensor decomposition]], have enabled their use in [[machine learning]] to embed higher dimensional data in [[artificial neural networks]]. This notion of tensor differs significantly from that in other areas of mathematics and physics, in the sense that a tensor is usuallythe regardedsame thing as a numericalmultidimensional quantityarray. inAbstractly, a tensor belongs to tensor product of spaces, each of which has a fixed basis, and {{clarify|text=the dimensiondimensions of the factor spaces alongcan thebe different. axes|reason=AnThus, axisan example of a tensor in this context is indexeda byrectangular matrix. Just as a scalarrectangular matrix has two axes, e.g.a horizontal and vertical axis to indicate the position of each entry, [[reala more general tensor has as many axes as there are factors in the tensor product to which it number]]belongs, [[complexand number]].}}an entry of the tensor needis notreferred to be thea sametuple of integers. The various axes have different dimensions in general.

== Generalizations ==