Discussion Overview
The discussion revolves around computing the eigenvalues of a large symbolic matrix (32x32) in Mathematica, focusing on the challenges encountered, particularly an error related to finding roots of the characteristic polynomial. The scope includes technical explanations and proposed methods for addressing the issue.
Discussion Character
- Technical explanation, Debate/contested
Main Points Raised
- One participant reports an error when attempting to compute eigenvalues for a 32x32 symbolic matrix in Mathematica, specifically related to the inability to find all roots of the characteristic polynomial.
- Another participant suggests trying both the Eigenvalues and Eigensystem functions, questioning which function produced the error and expressing skepticism about the difficulty of using Eigensystem for a single variable.
- A different participant proposes assuming ranges for the constants involved, indicating that this might help in resolving the issue.
- One participant notes that finding symbolic expressions for all 32 eigenvalues is inherently problematic due to the lack of a general method for solving 32nd order polynomials symbolically, suggesting that numerical methods may be more feasible.
Areas of Agreement / Disagreement
Participants express differing views on the feasibility of obtaining symbolic eigenvalues for the matrix, with some suggesting alternative approaches while others highlight the limitations of symbolic computation in this context. No consensus is reached on the best method to proceed.
Contextual Notes
The discussion reflects limitations in symbolic computation for high-order polynomials and the potential need for numerical methods, but does not resolve the specific mathematical steps or assumptions involved.