The principle of dimensional homogeneity, which asserts that any system of equations describing a physical phenomenon should be consistent with respect to physical dimensions, is shown to imply a kind of total unimodula¡ of the physically-dimensioned coeflicient matrix of the (linearized) system. This fact can be utilized in the structural approach to systems analysis in a number of ways; for example, it is useful in formulating some problems concerning dynamical systems in matroid-theoretic terms as well as in reducing the computational comptexity needed to solve them by combinatorial algorithms.