householder-givens

Let $x \in \mathbb{R}^2$ be a random vector then its rotation by $ \theta $ degrees is computed by Givens rotation method: $ \vec{x'} = \begin{pmatrix} c & -s\ s & c \end{pmatrix} \vec{x}$ , where $ c = \cos{\theta} $ and $s = \sin{\theta} $ and its reflection over a subspace orthogonal to a given unit vector $ v \in \mathbb{R}^2 $ is $ \vec{x''} = \vec{x}-2[(\vec{x} \cdot \vec{v}) \vec{v}] $.

Prerequisites

To run the application you need to have installed the python packages from requirements.txt.

Application

Application starts by running the app.py script.

• 🔵 : x
• 🟢 : x' / x'' (rotation/ reflection)
• 🔴 : orthogonal subspace