Math — Transformation Matrices

R(\theta) = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}

\text{reflect in } x\text{-axis}: \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}

\text{scale}: \begin{pmatrix} k & 0 \\ 0 & k \end{pmatrix}

\det = \text{area scale factor}