Applications of matrix algebra to communication nets

Abstract

A “generic” problem amenable to matrix algebraic treatment is outlined. Several examples are given and one, a communication system, is studied in some detail. A typical structure matrix is used to describe the channels of communication and a “status” matrix is used to describe the distribution of information in the system at any time. A theorem is proved relating the status matrix at any timet to thetth power of the structure matrix. The elements of the communication system are interpreted as individuals who can send messages to each other. For the individuals attempting to solve a “group problem” certain relations are derived between the structure and status matrices and time of solution. The structure of the communication system is permitted to vary with time. A general theorem is proved relating the status matrix to the matrix product of the series of structure matrices representing the changing structure of the system. Some suggestions are made for further generalizations. In particular, it is suggested that so-called “higher order” information transmission can be similarly treated.