Eigenvalues of partitioned matrices "generated" by a matrix with known eigenvalues

A method is shown which allows to compute the eigenvalues of an
mn
-dimensional square matrix
F
from the eigenvalues of an
n
-dimensional matrix
A
, if the m
²
submatrices of
F
are describable by convergent power series of
A
. As an illustration, matrices arising in a multivariable feedback control system are considered.