View article

In mathematical modeling, it is common to have an equation , where the exact form of is not known. This article shows that there are large classes of where almost all share the same properties. The classes we investigate are vector spaces of functions that satisfy the following condition: has “almost constant rank" (ACR) if there is a constant integer such that rank for “almost every" and almost every . If the vector space is finite dimensional, then “almost every" is with respect to the Lebesgue measure on , and otherwise, it means almost every in the sense of prevalence, as described herein. Most function spaces commonly used for modeling purposes are ACR. In particular, we show that if all of the functions in are linear or polynomial or real analytic, or if is the set of all functions in a “structured system", then is ACR. For each and , the solution set of is SolSet …