Tensor product of Hilbert spaces | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Tensor_product_of_Hilbert_spaces


00:00:35 1 Definition
00:03:31 1.1 Explicit construction
00:06:26 1.2 Universal property
00:08:25 1.3 Infinite tensor products
00:09:51 1.4 Operator algebras
00:11:56 2 Properties
00:13:17 3 Examples and applications



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SUMMARY
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In mathematics, and in particular functional analysis, the tensor product of Hilbert spaces is a way to extend the tensor product construction so that the result of taking a tensor product of two Hilbert spaces is another Hilbert space.  Roughly speaking, the tensor product is the metric space completion of the ordinary tensor product.  This is an example of a topological tensor product.  The tensor product allows Hilbert spaces to be collected into a symmetric monoidal category.