A Mercer Kernel is a kernel that is positive semi-definite. When a kernel
is positive semi-definite, one may exploit the kernel trick, the idea of
implicitly mapping data to a high-dimensional feature space where some
linear algorithm is applied that works exclusively with inner products.
Assume we have some mapping Φ from an input space X to a feature space H,
then a kernel k(u, v) = <Φ(u), Φ(v)> may be used to define the
inner product in feature space H.
Positive definiteness in the context of kernel functions also implies that
a kernel matrix created using a particular kernel is positive semi-definite.
A matrix is positive semi-definite if its associated eigenvalues are nonnegative.