📅 2024-12-02 — Session: Analyzed Matrix Conditions and Error Handling in SymPy
🕒 15:35–17:45
🏷️ Labels: Matrices, Sympy, Numerical Analysis, Programming, Condition Numbers
📂 Project: Dev
⭐ Priority: MEDIUM
Session Goal
The session aimed to analyze the conditions of lower triangular matrices and resolve programming errors in matrix manipulation using SymPy.
Key Activities
- Conducted a mathematical analysis of the condition numbers ( \text{Cond}_\infty ) and ( \text{Cond}_2 ) for lower triangular matrices as ( n ) increases, demonstrating their tendency towards infinity.
- Presented results for matrix ( A ) with ( n=3 ), including its inverse and infinity norms.
- Addressed a SymPy error related to matrix row assignment, providing corrected code to ensure compatibility with SymPy’s matrix objects and proper application of a lower triangular mask.
- Analyzed the sensitivity of matrix ( A ) through its condition number and explored a lower bound for ( \text{Cond}_\infty(A) ) using a singular matrix ( B ).
- Simplified the symbolic representation of matrix differences for further analysis.
Achievements
- Successfully demonstrated the increasing condition numbers for triangular matrices as ( n ) increases.
- Resolved SymPy matrix manipulation errors, enhancing code reliability.
- Provided a comprehensive analysis of matrix ( A ) and its numerical sensitivity.
Pending Tasks
- Further exploration of symbolic matrix differences and their impact on condition numbers.
- Additional analysis on the properties of the infinity norm with practical examples.