Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

it is of course true that every linear map between two vector spaces can be expanded by means of the tensor product.

For instance, the metric in General Relativity (mapping covectors to vectors) can be expanded as

[itex]g=\sum_{i,j}g^{ij}e_{i}\otimes e_{j}[/itex].

However, does this statement hold true when the linear operator maps betweeninfinitedimensional vector spaces?

Any help is very much appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Tensor product and infinite dimensional vector space

**Physics Forums | Science Articles, Homework Help, Discussion**