Second, α$_{1}$ = 2 , α$_{2}$ = 0 , then does not exist for any non-zero matrix S . Third, α$_{1}$ = 0 , α$_{2}$ = 2 , then does not exist, except if s$_{21}$ = s$_{22}$ = 0 , which is precluded for non-singular matrix S . Now that we see that some matrices of polynomials satisfy the CLDR property and some do not, we further characterize the difference between the two possibilities. Lemma 4.2. Given a matrix G ( y ) with the corresponding ¯ a, for any non-singular matrix S and a ′ = ( α ′ $_{1}$, ..., α ′ q ) with 0 ≤ α ′ 1 ≤ ... ≤ α ′ q ≤ ¯ α and q ∑ i =1 α ′ i = ¯ α either (i) CLDR property holds with this S and a $^{′}$, or (ii) no finite limit exists for or (iii) if a finite limit does exist [ diag ( λ α ′ i ) SG ( y/λ ) ] , rank lim λ →∞ [ diag ( λ α ′ i ) SG ( y/λ ) ] < q. (16) 20 lim λ →∞    λ 2 0 0 1    SG ( y/λ ) lim λ →∞    1 0 0 λ 2    SG ( y/λ )