Definition:Generalized Eigenvector
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Definition
Let $\mathbf A$ be a square matrix of order $n$.
Let $\lambda$ be a generalized eigenvalue of $\mathbf A$.
Hence:
- $\mathbf A \mathbf x = \lambda \mathbf B \mathbf x$
for:
- some non-zero vector $\mathbf x$
- some square matrix $\mathbf B$ of order $n$.
The vector $\mathbf x$ is known as the generalized eigenvector corresponding to $\lambda$.
Also see
- Results about generalized eigenvectors can be found here.
Linguistic Note
The word eigenvector 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