Identification of induction curves - LÓCSI, Levente (Studia Universitatis Babeș-Bolyai Mathematica, 2023)
Induction curves (induction surfaces, induction sets in general) were recently introduced to provide a visual aid to examine the fractions defining the norm of a matrix, along with the discovery and description of p-eigenvectors. In our current investigation we delve into an inverse problem, the identification of induction curves. Namely: could the elements of the matrix and the used power parameter p be reconstructed given the induction curve, i.e. the case of 2 × 2 matrices is examined. The analytic solution is not possible in most cases already in this planar setting, therefore numerical approximation methods shall be applied. Mathematics Subject Classification (2010): 15A83, 47A30, 65F20, 65F35.