The logic in computer science column

According to Dirac's bra-ket notation, in an inner-product space, the inner product (sic)x l y (sic) of vectors x, y can be viewed as an application of the bra (sic)xl to the ket ly (sic). Here (sic)xl is the linear functional ly (sic) (sic)x l y (sic) and ly (sic) is the vector y. But often - though not always - there are advantages in seeing ly (sic) as the function a a center dot y where a ranges over the scalars. For example, the outer product ly (sic) (sic)xl becomes simply the composition ly (sic) o (sic)xl. It would be most convenient to view kets sometimes as vectors and sometimes as functions, depending on the context. This turns out to be possible.While the bra-ket notation arose in quantum mechanics, this note presupposes no familiarity with quantum mechanics.