📅 2024-12-02 — Session: Matrix Condition Analysis and SymPy Error Resolution

🕒 15:35–17:45
🏷️ Labels: Matrices, Sympy, Numerical Analysis, Python, Matrix Condition, Error Resolution
📂 Project: Dev
⭐ Priority: MEDIUM

Session Goal

The session focused on analyzing the condition of lower triangular matrices and resolving errors in matrix operations using SymPy.

Key Activities

  • Analyzed the condition of lower triangular matrix ( A_n ) in terms of ( \text{Cond}_\infty ) and ( \text{Cond}_2 ), demonstrating their tendency to infinity as ( n ) increases.
  • Presented results for matrix ( A ) for ( n=3 ), including its inverse, infinity norms, and condition number.
  • Resolved a SymPy error related to matrix row assignment by converting lists to compatible Matrix objects and applying a lower triangular mask.
  • Reconstructed matrix ( A ) using individual entries to maintain the lower triangular structure.
  • Analyzed a singular matrix ( B ) to provide a lower bound for the condition number of ( A ).
  • Simplified the result of the difference between two matrices for further analysis.

Achievements

  • Successfully demonstrated the numerical sensitivity of matrix ( A ) through condition number analysis.
  • Corrected SymPy matrix manipulation errors and improved code structure.

Pending Tasks

  • Further analysis of symbolic matrix differences and their infinity norms.
  • Exploration of additional properties of matrix norms and conditions.