  In this paper, we present a characterization of compact quantum metric spaces
in terms of finite dimensional approximations. This characterization naturally
leads to the introduction of a matrix analogue of a compact quantum metric
space. As an application, we show that matrix compact quantum metric spaces are
stable under minimal tensor products and more specifically that matrix spectral
metric spaces are stable under the external product operation on unital
spectral triples. We present several noncommutative examples of matrix compact
quantum metric spaces.
