Mathematica: Eigenvalues for a large symbolic matrix

In summary, When trying to compute the eigenvalues for a 32x32 symbolic matrix with one variable in Mathematica, a user encountered an error stating that it was unable to find all roots of the characteristic polynomial. The possible solution suggested was to try using both Eigenvalues[ ] and Eigensystem[ ]. Additionally, it was suggested to assume ranges for the constants to make the computation easier. However, it was noted that there is no general way to symbolically solve for the roots of a 32nd order polynomial, so a numerical approach may be necessary.
  • #1
Scheherzaade
1
0
I'm trying to compute the eigenvalues for a 32x32 symbolic matrix (with one variable) in Mathematica. I get the following error:

Eigenvalues::eival: Unable to find all roots of the characteristic \
polynomial. >>


What could be a possible way to proceed?

Thanks,
Schez
 
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  • #2
Have you tried both Eigenvalues[ ] and Eigensystem[ ]? From which function did you get this error? If it's in one variable then I don't really see why Eigensystem wouldn't work.
 
  • #3
Try to assume ranges for the constants, i.e. greater than 0, less than 0, etc...
 
  • #4
Scheherzaade,

If you are trying to find symbolic expressions for all of the 32 eigenvalues then it is no surprise that it complains. There is no general way to symbolically solve for the roots of a 32nd order polynomial, which is essentially what you are asking it to do. Numerical approaches are of course feasible ...

jason
 
  • #5


There are a few possible reasons for this error message. One possibility is that the matrix is ill-conditioned, meaning that it has a large condition number and is difficult to compute the eigenvalues accurately. In this case, using a higher precision or numerical methods may help to improve the accuracy of the eigenvalues.

Another possibility is that the matrix may have complex eigenvalues, which would require using complex arithmetic in Mathematica. You can try using the command Eigenvalues[matrix, Cubics -> True] to specify that the eigenvalues should be computed using complex arithmetic.

If the matrix is very large, it may also be helpful to use parallel computing techniques in Mathematica to speed up the computation. This can be done by using the command ParallelEigenvalues[matrix].

Alternatively, you can try using other software packages specifically designed for computing eigenvalues of large symbolic matrices, such as Maple or MATLAB. These packages may have different algorithms and methods that could potentially give better results for your specific matrix.
 

1. What is Mathematica?

Mathematica is a powerful computational software program used for various mathematical, scientific, and engineering calculations. It has a wide range of functions and tools for data analysis, visualization, and modeling.

2. What are eigenvalues?

Eigenvalues are a set of numbers associated with a square matrix that represent the scaling factor of the eigenvectors of that matrix. They are important in many areas of mathematics, including linear algebra, differential equations, and physics.

3. How do I find eigenvalues for a large symbolic matrix in Mathematica?

To find eigenvalues for a large symbolic matrix in Mathematica, you can use the built-in function Eigenvalues[matrix]. This will return a list of the eigenvalues for the given matrix.

4. Can Mathematica handle large symbolic matrices?

Yes, Mathematica has the ability to handle large symbolic matrices efficiently. However, the time and memory required to compute eigenvalues for these matrices may increase significantly with their size.

5. Are there any limitations to using Mathematica for computing eigenvalues?

There are some limitations to using Mathematica for computing eigenvalues, such as the time and memory required for large matrices, and the accuracy of the results may be affected by symbolic computations. It is always recommended to check the results and compare them with other methods for validation.

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