Mixed-normalization spline Gram matrix
= Mixed-normalization spline Gram matrix
{title2=$G=D^{-1}H$}
For partition-normalized <B-splines> $N_i$ and integral-normalized $M_i=kN_i/(t_{i+k}-t_i)$, let $H_{ij}=(N_i,N_j)$ and $D_{ii}=(t_{i+k}-t_i)/k$. The mixed matrix $G_{ij}=(M_i,N_j)$ equals $D^{-1}H$. It is invertible whenever the splines form a basis and their support widths are positive. It need not be symmetric, unlike the ordinary <Gram matrix>.