= Canonical feature space of a positive-semidefinite kernel
{title2=$\phi(x)=[e_x]$}
On the finite formal span of symbols $e_x$, define $B(e_x,e_y)=k(x,y)$ and extend bilinearly. For a <positive-semidefinite kernel>, the null vectors of this <positive semidefinite bilinear form> form its <radical of a bilinear form>. Quotienting by that <linear subspace> gives an <inner product space> and <feature map> $x\mapsto[e_x]$ with $\langle[e_x],[e_y]\rangle=k(x,y)$. This construction works for degenerate and zero kernels.
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