Computing eigenvalues and eigenvectors of two symbolic matrices

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FAWAZ FAREAD AL BAKRI
回答： Christine Tobler 2024-3-18
Hello all,
How could I compute the generalized eigenvalues and eigenvectors of (A,B) matrices using MATLAB if both of them are symbolic?
[V,D] = eig(B,A);
where A & B are (5x5)
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Torsten
Torsten 2024-3-16
编辑：Torsten 2024-3-16
Not possible.
The symbolic eigenvalue computation is limited to the roots of polynomials of degree <= 4. The reason is that for polynomials of degree > 4, there is no explicit solution formula for their roots - only in special cases.
https://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem

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Christine Tobler
Christine Tobler 2024-3-18
eig does not support the two-input syntax for symbolic. For the call eig(B, A), if A is invertible you can instead solve eig(A\B).
About the matrix size of the input, you can call eig for sizes greater than 4, although this will not have an explicit solution outside of special cases.

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