[psb217]

To be fair, the "trick" part of the kernel trick involves implicitly transforming the data into a higher dimensional space and then fitting a linear function in that space. Ie, you're transforming the inputs so that a linear function from inputs to outputs fits better than if you didn't do the transform.

The "trick" allows you to fit a linear function in that higher dimensional space without any potentially costly explicit computation in the higher dimensional space based on the observation that the optimal solution's parameters can be represented as a sum of the higher dimensional representations of points in the training set.