Category:Definitions/Generalized Eigenvectors

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

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 $\lambda$.