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It is well known that the bivariate polynomial interpolation problem atdomain points of a triangle is correct. Thus the corresponding interpolationmatrix $M$ is nonsingular. L.L. Schumaker stated the conjecture, that thedeterminant of $M$ is positive. Furthermore, all its principal minors areconjectured to be positive, too. This result would solve the constrainedinterpolation problem. In this paper, the basic conjecture for the matrix $M$,the conjecture on minors of polynomials for degree <=17 and for some particularconfigurations of domain points are confirmed.

On positivity of principal minors of bivariate Bezier collocation matrix