With x NMuV what are the necessary and sufficient condition

With x ~ N(Mu,V) what are the necessary and sufficient conditions for x?A1x + b\'1x + c1 and x\'A2x + b2\'x + c2 to be independent? What are these conditions when V is non-singular?

Solution

The Vandermode matrix V = (xi)j arises in the polynomial f(x) = an-1xn-1+ ....+a1x + a0 evaluation/interpolation problem at the n points xn,....x1, x0. The regular matrix representation A = (xiq^i) arises in the determination of linear independence and other properties of a subset of elements {xn,....x1, x0}