Hi all - basic question here, since I've mostly just confused myself.
I'm trying to disambiguate 'product' and 'outer product' in the context of bra-ket notation, and Hilbert spaces.
If I have kets |a> and |b>, what operation is performed in constructing |a><b|?
We call the result an "outer product", but it's incorrect to notate this as |a> (otimes) <b| where (otimes) is the tensor/kronecker product (also referred to as the outer product sometimes, confusingly). Instead, if |a> and |b> were vectors, the matrix |a><b| is just constructed from matrix multiplication of |a> and conjugate-trans…