Discussion Overview
The discussion revolves around the challenge of finding eigenvalues of a complex 12x12 matrix, with a focus on transforming the matrix into an upper triangular form. Participants explore methods and tools, particularly MATLAB and Mathematica, to achieve this transformation and compute eigenvalues.
Discussion Character
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant expresses difficulty in finding eigenvalues of a complicated 12x12 matrix and seeks guidance on how to convert it to upper triangular form using MATLAB or Mathematica.
- Another participant suggests using built-in functions for eigenvalues instead of transforming the matrix, questioning the necessity of diagonalization.
- A participant claims that MATLAB and Mathematica are unable to handle the complexity of the matrix for eigenvalue calculations.
- QR decomposition is proposed as a method for obtaining an upper triangular matrix, with references to relevant functions in both MATLAB and Mathematica.
- One participant clarifies that their matrix is symbolic, indicating that QR decomposition may not be suitable for their needs.
- A later reply expresses skepticism about obtaining symbolic solutions for the eigenvalues of a 12x12 matrix, suggesting that the complexity increases significantly compared to smaller matrices.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the best approach to take. There are competing views on whether to transform the matrix or directly compute eigenvalues, and uncertainty remains regarding the capabilities of the software for symbolic matrices.
Contextual Notes
Limitations include the complexity of the matrix and the potential inadequacy of software tools for symbolic computation. Participants note that methods like QR decomposition may not apply to symbolic matrices.