In an earlier paper of mine relating vector bundles and Gromov-Hausdorff
distance for ordinary compact metric spaces, it was crucial that the Lipschitz
seminorms from the metrics satisfy a strong Leibniz property. In the present
paper, for the now non-commutative situation of matrix algebras converging to
the sphere (or to other spaces) for quantum Gromov-Hausdorff distance, we show
how to construct suitable seminorms that also satisfy the strong Leibniz
property. This is in preparation for making precise certain statements in the
literature of high-energy physics concerning "vector bundles'' over matrix
algebras that "correspond'' to monopole bundles over the sphere. We show that a
fairly general source of seminorms that satisfy the strong Leibniz property
consists of derivations into normed bimodules. For matrix algebras our main
technical tools are coherent states and Berezin symbols.