Now we prove . Set . Then (since and are triangular and is satisfied for L U A(k) k=n) . From the definitions of we get and recall that . Thus, if then ij, . When . i>j, Finally, we prove . Let . So, .
Now we prove . Set . Then (since L and U are triangular and A(k) is satisfied for k=n) . From the definitions of we get and recall that . Thus, if ij, then . When i>j, . Finally, we prove . Let . So, .
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