Finite-rank projection kernel
= Finite-rank projection kernel
{title2=$K(x,y)=\sum_{j=0}^{m-1}\phi_j(x)\overline{\phi_j(y)}$}
An <orthonormal set> $\phi_0,\ldots,\phi_{m-1}$ in an $L^2$ space defines the <integral kernel> of the <orthogonal projection> onto its span by this sum. It satisfies $\int K(x,y)K(y,z)\,d\mu(y)=K(x,z)$ and $\int K(x,x)\,d\mu(x)=m$. Its evaluation <matrices> are positive semidefinite Gram <matrices>.