# What is "dual form"

I am reading up on AI and now read https://en.wikipedia.org/wiki/Kernel_perceptron

It says:

To derive a kernelized version of the perceptron algorithm, we must first formulate it in dual form, starting from the observation that the weight vector w can be expressed as a linear combination of the n training samples.

But what is "dual form"?

The word "dual" is widely used throughout mathematics. The meaning of the word depends on the context, and usually refers to the object whose properties are reversed. In the above context, it means that the problem of finding $$\mathbf{w}$$ has been reversed to the problem of finding $$\alpha$$.