# Is this a decent summary of the kernel trick?

Here's my understanding of the kernel trick. The motivation is to find a linear separator in a higher dimensional space than what you have (because the data are not currently linearly separable.) You take the dot product, and then apply the transformation to the result, saving you the time of applying the transformation to each of the pieces of data going into the dot product.

Is this a decent summary or am I missing something?

Thanks

Yes. Simply put, $k(x,y) = <\Phi(x), \Phi(y)>$ is the kernel trick. Inner product in the feature space is the evaluation of kernel in the input space.