📅 2024-08-29 — Session: Change of Basis Matrix Calculation and Verification
🕒 17:45–18:00
🏷️ Labels: Linear Algebra, Python, Change Of Basis, Matrix Calculations, Numpy, Sympy
📂 Project: Teaching
⭐ Priority: MEDIUM
Session Goal
The session aimed to explore and implement the change of basis matrix calculations between different vector spaces, focusing on both theoretical understanding and practical implementation using Python.
Key Activities
- Change of Basis Matrix Calculation and Error Analysis: Explored the process of calculating the change of basis matrix from one basis to another, identifying potential errors in the transformation process.
- Python Implementation: Developed Python code to compute the change of basis matrix, including debugging and verification steps.
- Inconsistency Diagnosis: Analyzed and diagnosed inconsistencies in vector transformations, detailing computations and potential error sources.
- Verification: Implemented a Python script to verify change of basis transformations using NumPy, ensuring accurate vector transformations between bases.
- Advanced Techniques: Utilized NumPy and SymPy for streamlined change of basis calculations, providing example code for efficient implementation.
Achievements
- Successfully calculated and verified change of basis matrices using both manual and Python-based methods.
- Identified and addressed potential errors in the transformation process, improving accuracy and reliability.
Pending Tasks
- Further exploration of advanced matrix operations and optimizations using Python libraries.
- Implementation of additional test cases to ensure robustness of the change of basis calculations.