Classification of Kernels (IEL4)

Kernels are classified based on the following criteria:

1. Separable/Degenerate: $K(s,t) = \sum a_i(s)b_i(t)$
2. Symmetric or Hermitian: $K(s,t) = K^*(t,s)$, where * denotes the conjugate
3. Convolution Type: $K(s,t) = K(s-t)$

Note that a kernel may be of two types at the same time.

For example, $K(s,t)=s-t$ is of both separable and of convolution type. It is not symmetric as $K(t,s)\ne K(s,t)$. You will find more examples in the quiz (link).

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