To any given n × n matrix D, associate a so-called tower matrix T with n × n rows and n columns. This matrix T deserves attention because it gives more information than D: in fact, the tower matrix exhibits, not only the shortest length of the paths from point p to point q, but also, for each third point k, the shortest length of the paths from p to q that pass through k. Interpretations of interest for business management and international commerce, for instance, emphasize the advantage of this supplementary information.