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I'm digging into SVM's, and there is a certain step which is not all clear to me, and it is the part of representing $W$ as a linear combination of the training examples. How can we suppose that this is always possible? Aren't there problems if the training examples are linear combinations of each other, or when there are more features than examples?

$$ f(x) = \vec w^\intercal \vec x + b \\ \vec w = \sum_i^n \alpha_i \vec x_i \\ f(x) = \sum_i^n \alpha_i \vec x_i^\intercal \vec x + b $$

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