Definition:Generalized Eigenvalue
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Definition
Let $\mathbf A$ and $\mathbf B$ be square matrices of the same order.
Let $\lambda$ be a number such that:
- $\mathbf A \mathbf x = \lambda \mathbf B \mathbf x$
for some non-zero vector $\mathbf x$.
Then $\lambda$ is a generalized eigenvalue of $\mathbf A$.
Also see
- Results about generalized eigenvalues can be found here.
Linguistic Note
The word eigenvalue derives from the German eigen, meaning characteristic, or (literally) own.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generalized eigenvalue