I a * 1 = ∑ ( aj 1 + a∣ 2 ) and IA * * 1 = ∑ ( a j + a 2 j ) for j = 3, 4, ■■■■ N
Based on the degree of autonomy, a degree of block dependency can be defined as:
Gd(A*)=1-Ga(A*)
It is easy to see that in a matrix A of order N there are 2n - 2 blocks A* (because there are
∑(kN ) blocks A* with k = 1, ... , N-1).
So, the degree of (raw) dependency of system A is defined as:
∑kGd(Ak*)
for which k varies from 1 to 2N - 2 and Ak* represents a square block that includes the main
diagonal.
After correcting by the scaling factor given by the maximum value of G*(A) (which is a
function of N):
2 n — 2 n-2 — ι
2 n — 2
the dependency degree G(A) of A is:
11
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