  Given a compact metric space X and a unital C*-algebra A, we introduce a
family of seminorms on the C*-algebra of continuous functions from X to A,
denoted C(X, A), induced by classical Lipschitz seminorms that produce compact
quantum metrics in the sense of Rieffel if and only if A is finite-dimensional.
As a consequence, we are able isometrically embed X into the state space of
C(X,A). Furthermore, we are able to extend convergence of compact metric spaces
in the Gromov-Hausdorff distance to convergence of spaces of matrices over
continuous functions on the associated compact metric spaces in Latremoliere's
Gromov-Hausdorff propinquity.
