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## Main Question or Discussion Point

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

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