Refactor RKHS document for clarity and formatting improvements

RKHS.md

@@ -5,12 +5,7 @@
 Let `X` be a non empty set. Let $k: \mathbb{X} \times \mathbb{X} \to \mathbb{R}$ symetric and positive definite. 
 
 
-$$
-\forall (x_{1}, ..., x_{n}) \in \mathbb{X}^{n},
-\forall c \in \mathbb{R}^{n},
-
-\sum_{i=1}^{n} \sum_{j=1}^{n} c_{i} c_{j} k(x_{i}, x_{j}) \geq 0
-$$
+$\forall (x_{1}, ..., x_{n}) \in \mathbb{X}^{n}, \forall c \in \mathbb{R}^{n}, \sum_{i=1}^{n} \sum_{j=1}^{n} c_{i} c_{j} k(x_{i}, x_{j}) \geq 0$
 
 $ K_{i, j} = k(x_{i}, x_{j}) $
 
@@ -24,4 +19,12 @@ Let `H` be a Hilbert space of functions of real value functions $ f: \mathbb{X}
 `H` is called the Reproducing Kernel Hilbert Space (RKHS) associated to `k`.
 
 
-**remark:** $ f = K(., x) then k $
+**remark:** $ f = K(., x), k(x, x') = \langle k(., x'), k(., x) \rangle_{H} $
+
+## Examples of kernels
+
+### kernel PDS
+
+- $k(x, x') = \exp(-\gamma \|x - x'\|^2) $ with $ x, x' \in \mathbb{X} $
+- $k(x, x') = (1 + \langle x, x' \rangle)^{p} $ with $ x, x' \in \mathbb{X} $
+