B-spline collocation matrix

For B-splines $N_j$ and interpolation sites $x_i$, the B-spline collocation matrix is $A_{ij}=N_j(x_i)$. Its invertibility is the existence-and-uniqueness condition for interpolation in that B-spline basis.

For increasing interpolation sites $x_i$ and an order-$k$ B-spline basis with knots $t_i$, the B-spline collocation matrix is invertible exactly whenfor every $i$, equivalently when $N_i(x_i)>0$ for every $i$.