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##

Let us continue with , likewise labelling its rows and
columns by the 2-blocks to which they correspond. Zero matrix
elements---for which there is no link in the de Bruijn diagram---will
be suppressed in favor of dots.

.3em

**Figure:** Two stage binary de Bruijn matrix and diagram.

By a simple calculation,

which is a minimal
equation rather than a characteristic equation since it is not of degree
4. Its roots are . is evidently singular because
of the repeated rows, but on closer inspection we find that it shows the
Jordan canonical form with respect to a block belonging to
eigenvalue 0.

The matrix of principal vectors reducing to canonical form could be

The first three columns are eigenvectors, the last a principal vector.

Although characteristics of the de Bruijn matrices are already evident
in , it is worth going on to examine for good measure.

* Harold V. McIntosh *

E-mail:mcintosh@servidor.unam.mx