In this note some of the interesting work on the synthesis problem of electrical network theory is translated into ordinary algebraic language. A function f(z) of a complex variable z is positive real in the sense of Brune if f(z) is a rational function with real coefficients such that Re f(z) _ 0 for Re z _0. (PR is an abbreviation for positive real.) Starting with PR functions it is obvious that the following operations lead to new PR functions: (a) Multiplication by a positive constant or zero, cf(z); (b) Forming the inverse, l/f(z); (c) Addition, f,(z) +f2(z). The zero function is PR and operation (b) is excluded in this case. Starting with the PR functions 1 and z as a basis, it follows that the operations (a), (b), and (c) generate a subclass of the PR class. It is a consequence of a synthesis method given by Bott and Duffin [1 ] that actually any PR function can be so generated. This observation is due to Brockway McMillan. In this note it is shown that the class of positive real matrices may be generated in an analogous fashion. A positive real matrix function F(z) is defined as follows: I. F is an n by n symmetric matrix. II. The matrix elements F1k are rational functions of z with real coefficients. III. For any choice of complex numbers cl, c2, ,n