Matrix Exponential Visualizer

An interactive Python notebook that visualizes the matrix exponential in real-time for $2 \times 2$ matrices. Built as a conceptual tool to illustrate the flow generated by a matrix in the plane, this project bridges linear algebra, differential equations, and Lie group theory.

This visualization tool was developed as part of the Lie Groups with Applications course with Quantum Formalism, and is ideal for students, researchers, and instructors looking to understand:

• How to compute the matrix exponential numerically
• How to visualize matrix Lie groups through their action on vectors
• The role of the exponential map in Lie group structure
• Real-time animation using matplotlib and ipywidgets

Features:

• Interactive sliders for adjusting entries of a real $2 \times 2$ matrix
• Dynamic vector field updates and trajectory overlays
• Modular code structure for reuse in teaching notebooks

GitHub:
MatrixExponential