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##

Let us start with , which is a matrix (showing a
border identifying the 1-blocks which have been linked).

.5em

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

The simple structure is due to the fact no matter whether 0 or 1 is
dropped from a 1-block, or whether 0 or 1 is added to the block, the
maneuver is feasible; thus all positions of the matrix are filled with
a one. By inspection, we see that

which is the characteristic equation for . It has eigenvalues
. Since it is symmetric it has an orthogonal eigenvector
matrix, which is:

The coefficient rather than is chosen because we
will presently use probability vectors, which are normed by sums of
absolute values rather than sums of squares.

* Harold V. McIntosh *

E-mail:mcintosh@servidor.unam.mx