Some unitarity bounds for finite matrices

Abstract
We study the problem of obtaining the bounds on the modulus of one element of a finite unitary matrix once the values of the moduli of a set of other elements are given. The problem is solved in simple cases, and indications of more general cases are given. This question is interesting from a physical point of view since it leads to direct inequalities between sets of partial waves. It would also be useful to extend this kind of results to the continuous matrices where inequalities on cross sections could be obtained.

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