  An odd Fredholm module for a given invertible operator on a Hilbert space is
specified by an unbounded so-called Dirac operator with compact resolvent and
bounded commutator with the given invertible. Associated to this is an index
pairing in terms of a Fredholm operator with Noether index. Here it is shown by
a spectral flow argument how this index can be calculated as the signature of a
finite dimensional matrix called the spectral localizer.
