Category:Definitions/Generalized Eigenvalues

This category contains definitions related to Generalized Eigenvalues.
Related results can be found in Category:Generalized Eigenvalues.

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 $\mathbf A$.