Developed and Corrected Matrix Operations for Linear Algebra

📅 2024-09-12 — Session: Developed and Corrected Matrix Operations for Linear Algebra

🕒 17:25–18:50
🏷️ Labels: Matrix Inversion, Gaussian Elimination, Github, Education, Python
📂 Project: Teaching
⭐ Priority: MEDIUM

Session Goal

The goal of this session was to develop, implement, and correct matrix operations related to linear algebra, focusing on educational applications and accuracy in numerical methods.

Key Activities

• Proposed an exam exercise for students to evaluate their understanding of matrix operations such as inversion, base change, and solving linear systems using matrix echelon methods.
• Implemented and tested Python functions for row echelon transformation and matrix inversion, addressing numerical precision issues using np.allclose for verification.
• Developed code for matrix inversion using back substitution and Gaussian elimination, ensuring accuracy in the inverse matrix.
• Explored base change in vector spaces, including matrix construction and transformation of vectors between bases with Python examples.
• Created exercises involving matrix inversion, Gaussian elimination, and base change for educational purposes.
• Organized student assignment submissions using GitHub, detailing repository setup, submission processes, and code review without pull requests.
• Corrected issues in Gaussian elimination code, ensuring proper storage of reduction factors in matrix L and successful LU decomposition.

Achievements

• Successfully implemented and corrected matrix operations for educational use, including Gaussian elimination and LU decomposition.
• Established a structured method for student submissions via GitHub, enhancing the educational workflow.

Pending Tasks

• Further refine the numerical precision handling in matrix operations.
• Explore additional educational exercises to reinforce student understanding of linear algebra concepts.