solve symbolic eigenvalue problem

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liad
liad 2025-2-3
编辑： Torsten 2025-2-15
Hello everyone,
I have a system of linear equations in the following form: AX=BX
where matrix A is constructed from values of the parameter a,
and matrix B consists of eigenvalues.
Each eigenvalue solution should be dependent on a.
I want to find, for each eigenvalue, the smallest value and the corresponding aaa that satisfies it.
I attempted to solve this using the syms and eigs functions but was unsuccessful.
My main difficulty lies in defining symbolic parameters and then using them after solving for the eigenvalues.

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回答（1 个）

Torsten
Torsten 2025-2-3
编辑：Torsten 2025-2-3
Ran in:
If you want an analytical expression for the eigenvalues dependent on the parameter a, your matrix A must have dimension <= 4.
syms a
A = [a a^2;2 exp(a)];
eig(A)
ans = 
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liad
liad 2025-2-15
Thank you for your response.
So I have a problem because I have a sixth order differential equation that looks in matrix form Ax=Bx. When matrix A depends on some parameter. And matrix B can be defined as the matrix of the eigenvalues. I solve the equation using finite elements so I need about 100 equations to get good accuracy. The thought was to solve it like an eigenvalue problem, but my matlab only manages to calculate 20 x 20 at most. Is there any way to solve the system? Maybe not through eigenvalues?
Torsten
Torsten 2025-2-15
编辑：Torsten 2025-2-15
Just out of curiosity:
Why do you get a matrix A depending on a parameter if you discretize a differential equation ?

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