Eigentest is a collection of routines to create and manipulate
test matrices, called eigenmats, with known eigenvalues and
eigenvectors.  Eigenmats are real matrices maintained in factored form
in such a way that storage and operation costs are proportional to the
order of the eigenmat in question.  The spectrum of an eigenmat
consists of real eigenvalues, complex conjugate pairs of eigenvalues,
and real Jordan blocks.  The operations consist of multiplying a
matrix by $(A-sI)$, $(A-sI)\trp$, $(A-sI)\inv$, and $(A-sI)\itp$,
where A is the eigenmat and $s$ is a shift.  In addition, {\Eigentest}
provides a function to compute individual eigenvectors and principal
vectors, and functions to help with the creation of eigenmats.

The Eigentest packages provides implementations in four languages: C,
Fortran77, Fortran95, and Matlab, which are contained in the directories
c, f77, f95, and matlab.  The subdirectories contain user guides with
details specific to the language in question.


Che-Rung Lee
G. W. Stewart
Nov  9 2007

