Definition:Generalized Eigenvalue

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