Why is $k$ called representor of evaluation? From the book "Learning with kernels" by Bernhard Schölkopf we have the following lines (page 33):
$\langle k(.,x),f\rangle = f(x)$, in particular $\langle k(.,x), k(.,x')\rangle = k(x,x')$
According to the book this interesting property of $\phi$ follows from definition. How?
I am unable to understand this and this is crucial for understanding the concept of reproducing kernel Hilbert spaces. Any help appreciated.
Luckily, the part of the book which needs to be referred i.e. section 2.2.2 (starts on page 32) is a part of the preview in Google books. Also note that this section is independent of other sections.