Generalized Non-Hermitian Eigenproblems

We assume that and are general by matrices.
We call
a *matrix pencil*, or *pencil* for short.
The most common case, and the one we will deal with first,
is the *regular case*, which occurs when and are square
and the *characteristic polynomial*
is not zero for
all .^{}This is equivalent to assuming that there are eigenvalues
(finite or infinite) and that they are
continuous functions of and , i.e., that small changes
in and cause small changes in the eigenvalues
(this requires an appropriate definition for the case of
infinite eigenvalues).

We will deal with the singular case at the end of this section.

- Eigenvalues and Eigenvectors
- Deflating Subspaces
- Equivalences
- Eigendecompositions
- Conditioning
- Specifying an Eigenproblem
- Related Eigenproblems
- Example
- Singular Case

Susan Blackford 2000-11-20