Here is a series of course notes migration, in order to say-goodbye to the text books and my messy physical notepads.

Hypothesis model

$$H_\theta(X) = \theta^T X = \theta_0\cdot 1 + \theta_1\cdot x_1 + \cdots + \theta_n\cdot x_n$$ $\theta\in n+1$ column vector, $X\in (n+1)\times m$ matrix when having $m$ training cases.

Cost function

$$J(\theta) = \frac{1}{2m} \sum^m_{i=1} (H_\theta(X^{(i)}) - y^{(i)})^2$$