linear algebra

$$\scriptsize \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} w & x \\ y & z \end{pmatrix} = \begin{pmatrix} aw + by & ax + bz \\ cw + dy & cx + dz \end{pmatrix}$$

$$\det(A)$$

$$proj_{\vec{b}}(\vec{a})=\frac{\vec{a}\cdot\vec{b}}{\|\vec{b}\|^2}\vec{b}=(\vec{a}\cdot\hat{b})\hat{b}$$

$$\vec{a} \times \vec{b} = \begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}$$

$$\vec{a} \cdot \vec{b} = \sum_{i=1}^n a_i b_i$$