  By the use of Perron-Frobenius theory, simple proofs are given of the
Fundamental Theorem of Demography and of a theorem of Cushing and Yicang on the
net reproductive rate occurring in matrix models of population dynamics. The
latter result is further refined with some additional nonnegative matrix
theory. When the fertility matrix is scaled by the net reproductive rate, the
growth rate of the model is 1. More generally, we show how to achieve a given
growth rate for the model by scaling the fertility matrix. Demographic
interpretations of the results are given.
