Let $w$ be the decision boundary of a linear SVM trained on the dataset $D=\{(x_i, y_i)_{i=1}^N\}$. Suppose we apply a linear transformation A to examples $x_i$s and obtain a new dataset $D'=\{(z_i, y_i)_{i=1}^N\}$ where $z_i = Ax_i$. And let $w_2$ denote the decision boundary of the linear SVM trained on $D'$.
Can we say anything about the relationship between $w$ and $w_2$? Depending on the properties of $A$, would it be possible to cheaply obtain $w_2$ from $w$?
