Question

(b) For two classes $i$ and $j$ ($i \neq j$), show that the decision boundary between the two classes (i.e., $g_i(x) = g_j(x)$) is described by a hyperplane, $w^T x + b = 0, \quad (6.19)$ $w = \Sigma^{-1}(\mu_i - \mu_j), \quad b = -\frac{1}{2}(\mu_i + \mu_j)^T \Sigma^{-1} (\mu_i - \mu_j) + \log \frac{\pi_i}{\pi_j} \quad (6.20)$