reproducingkernel
A reproducing kernel, in the context of functional analysis, is a function K: X × X → F associated with a reproducing kernel Hilbert space H of functions on X. It has the reproducing property: for each x in X there exists a function Kx(·) in H such that f(x) = ⟨f, Kx⟩H for every f in H. The kernel is symmetric and positive definite, and K(x, y) = ⟨Ky, Kx⟩H.
This property implies that evaluation at a point is a continuous linear functional on H, and the
Common examples include the linear kernel K(x, y) = x·y, the polynomial kernel (x·y + c)^d, and the
In practice, reproducing kernels underpin kernel methods in machine learning, such as support vector machines, kernel