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

I've read the math that defines a tensor product by means of the universal property and I've studied the tensor product construction through a quotient of the free vector space on the cartesian product of two vector spaces. All other constructions of the tensor products are naturally isomorphic to this in a natural way.

The problem I still have is what follows. If we have two concrete vector spaces in quantum mechanics what shall we do? Suppose they are finite dimensional. How do I construct the tensor product in a "real life" situation?

The answer I give to me after all the above math is:

(a) either for some physical reason, or bright idea dreamt up while sleeping, I'm able to come up with a concrete definition of "v tensor w" from to given vectors v and w (then I know, from the above math, that this is unique up to an isomorphism), or

(b) I work somehow more formally, using all the properties of tensor products and their linear mappings, reassured that the above math gives a rigorous foundation to this mathematical tool I'm using.

Do I get anything right?

Kindest regards.

Goldbeetle

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# Tensor product of vector spaces: confusion

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