Chacteristic equation
Unfortunately information about the other eigenvalues, particularly the second largest of them, is not so readily available---either directly or from the factored forms. However, formulas for the coefficients of the characteristic equation can be derived from the symbolic form of the de Bruijn matrix elements; their expression is even more elegant if a new rule of composition is introduced for regular expressions, particularly for sequences of symbols.
Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx