determinantal

In the 1970's, I continued theoretical work in crystal structure analysis that included the derivation of a "tangent formula" for phase determination that was based on the more restrictive higher and higher order determinants from the determinantal inequalities.

Jerome Karle - Autobiography 1986

I also derived heuristic joint probability distributions based on the determinants involved in the determinantal inequalities and obtained from them formulas for evaluating triplet phase invariants and, later on, formulas for the expected values of phase invariants and embedded semi-invariants of any order, triplet, quartet, quintet, etc. The utility of phase invariants of high order in phase determination has so far been rather limited, except perhaps collectively in the high order determinants where they have been useful for refining the values of approximately determined phase values.

Jerome Karle - Autobiography 1986