The matrix representation of a diagram can be factored into a product
of matrices, generally rectangular, which relate the nodes and links to
one another, rather than nodes to nodes or links to links. Using capital
letters for links, small letters for nodes, the matrix elements of the
factors are generally boolean propositions such as ``node a lies at the
tip of link B.'' Then the node linking matrix is the product
,
whilst the link joining matrix is 
, or
Figure 5 shows a diagram upon which its dual has been
superimposed; the 
factorization for 
is:
0.4em
Reversing the order of the factors produces 
:
0.4em
There is a temptation to repeat the process to obtain a series of higher order duals; likewise one wonders about the reverse, whereby a given diagram could be exhibited as the dual of another.