Is there a solution for the problem:
$$ (A_0 + \alpha \ A_1 + \beta \ A_2 ) x = 0 $$ where: $ A_0, A_1,$ and $A_2 \in \mathbb{R}^{n\times n}$, $\alpha$ and $\beta \in \mathbb{C}$, and $x \in \mathbb{C}^{n \times 1}$
Solving the two-parameter generalized Eigenvalue problem
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matrices
eigenvalues-eigenvectors
matrix-equations
matrix-decomposition
weighted-least-squares
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0Solving for $x$, $\alpha$ and $\beta$ – 2017-02-10
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0Well, there isn't a closed form solution even if you enforce $A_1=I$ and $\beta=0$, so... – 2017-02-10
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0if $\beta = 0$ then it becomes a generalized eigenvalue problem $A_0 \ x = -\alpha A_1 \ x$ which can be solved using generalized Schur decomposition, however I don't know the solution/approach when ($\alpha , \beta \ne 0$) – 2017-02-11
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0It's not clear how the solution can be posed, though, if you allow for non-closed-form operations like Schur decompositions. – 2017-02-11