In search of a meaning of determinant

This research introduces three operators, the bisection surface determinant, the rational surface determinant and the real surface determinant, for arbitrary functions defined on a closed rectangle S. Each determinant is the limit of a sequence of determinants of matrices corresponding to values of the considered function in a recursively generated grid of S. Some properties are found and an algorithm is provided. This research is still at an initial stage, although applications to functional analysis are expected and, therefore, to functions representing phenomena in Economics and Finance.