= Determinant criterion for a Chebyshev system
{title2=$\det(u_j(x_i))\ne0$}
A family of $n+1$ real <continuous functions> is a <Chebyshev system> exactly when every evaluation <matrix> at $n+1$ distinct points is invertible. A singular evaluation matrix supplies a nonzero coefficient vector whose function vanishes at those points; conversely, a violation of the zero bound supplies such a vector in the <kernel>. This also gives the existence and uniqueness of interpolation from its span.
Back to article page
