# Difference between the outer product

Dragonfall
Given $$\left| v\right>$$ and $$\left| u\right>$$ what is the difference between the outer product $$\left| v\right>\left< u\right|$$ and the tensor product $$\left| v\right>\otimes\left|u\right>$$? Is the latter a matrix representation of the former in some basis? Which basis would that be?

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I meant the tensor product $$\left< v\right|\otimes\left| u\right>$$.