"Bruno Luong" <email@example.com> wrote in message <firstname.lastname@example.org>... > A distance is simply the norm of the difference. This is standard definition of Banach's space (matrices is a banach's space), something that is very familiar to mathematicians . - - - - - - - - - - To be a valid "distance" it is only necessary to demonstrate that the norms of matrix differences satisfy the simple axioms for a metric space. The facts that this particular metric is complete and that we have a vector space is unneeded.
However, Simran's use of the adjective "minimum" suggests that perhaps a somewhat different meaning was intended.