  In these notes we review the calculation of Jones polynomials using a matrix
representation of the braid group and Temperley-Lieb algebra. The pseudounitary
representation that we consider allows constructing ``states'' from the
group/algebra matrices and compute the knot invariants as matrix elements,
rather than traces. In comparison with a more standard way of computing the
invariants through traces, the matrix element method is more interesting and
complete from the point of view of applications. As a byproduct of the
discussion we prove a general formula for pretzel knots.
