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I have encountered the concept of tensor product between two or more different vector spaces. I would like to get a more intuitive sense of what the final product is.

Say we have two vector spaces ##V_1## of dimension 2 and ##V_2## of dimension 3. Each vector space has a basis that we have choose among the many possible ones. For ##V_1## the basis set is ##a_n=(a_1, a_2))##.

For ##V_2## the basis set is ##b_n=(b_1, b_2, b_3))##.

The tensor product between ##V_1## and ##V_2## is $$V_3= V_1 \otimes V_2$$

What type of vectors live in this new vector space ##V_3##?

What can we say about the basis for the vector space ##V_3##?

What is the idea behind calculating the tensor product the two vector spaces? What are we trying to capture?

Thanks for any insight,

Fog37

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# I Understanding tensor product

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