Definition:Generalized Eigenvector

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