Intervals of P-matrices and related matrices (Q797660)

First, necessary and sufficient conditions for an interval matrix are given to contain no other matrices but P-matrices, that is, matrices having only positive principal minors. Similar statements for some other classes of matrices are posed then. Second, applications of the derived assertions to some problems of analysis and optimization are given, for instance, how to use P-matrices in order to manifest differentiable functions to be globally univalent, or to prove the unique solvability of the linear complementarity problem where the coefficient matrix is not exactly known.