A parametric interval matrix is a matrix whose elements are functions of unknowns whose values lie in some pre-defined ranges. It is therefore a matrix that has a higher structure than the classical interval matrix (i.e. matrices whose elements are intervals) as there may be dependency between the elements of the matrix.
A sophisticated procedure to check for the regularity of a parametric matrix is based on the following scheme: the sign of the determinant is calculated for a point value of the input parameters (say positive), then the algorithm try to find another input value such that the sign of the corresponding determinant is negative.