We have seen that every outer product (ketbra), or sum of outer products, be- haves like an operator, and that any operator can be expressed as a sum of outer products. Show that some operators can't be expressed as a single outer product. In other words, find an operator that can't be written as la){| for any possible Ja) and ().

[Hint: Since this is an existence proof, it suffices to find a specific example of such an operator, perhaps in a 2-D or 3-D Hilbert space using a matrix representation.]