54 Pedodiversity
expressed by a natural number) in which the n
i
objects of one class defi ne
a submatrix Ri(n
i
xn
i
) is the basis to calculate the diversity of a partition
C(O). According to this view, when R(TxT) is a crispy matrix, i.e., the
submatrices are completely disjointed (complete similarity within the S
classes of the objects and zero similarity between the classes) the n
i
are the
eigenvalues of R(TxT). In this situation the evenness of these eigenvalues
is equal to the formulas 17) and 18) that are expressing the relative measure
of heterogeneity of R(TxT). It is easy to prove that when R(TxT) is not a
crispy matrix the evenness of the eigenvalues of R(TxT) is lower than that
of the corresponding crispy matrix (Wilkinson 1965, Noy-Meir ...