17
We shall show that Ьц ≤ ∣M∣ implies ∖bji∖ < bjj. System ( 4.1) also implies that
∏+1
ɪɪ) λibih = 0,h = 1,∙ ∙ ∙ ,n.
i=l
It is easily derived that
a,∙m ≥ aj∙ ∣m ∣
and
MIMI — λjbjj.
Notice that at least one of the above inequalities holds with strict inequality, say,
λiba > Aj ∖bij ∣. Moreover, it holds that A8M ≤ Λ√∣6√7-1. All of this together implies
that
Aj∣M∣ < AiM ≤ a⅛j∣ ≤ AjM.
It follows that
∣M∣ < Mj-
We are now ready to prove that the new generated column j, denoted by
(M', ’ ’ ’ 5 M-+∣)√ M∙ preserves the same sign pattern as before. Note that
Mj = Mj + сМг, A = 1, , И + 1.
It is readily seen that
M = — d ≤ 0 and ∣M∣ < M'
Mj ≤ θ for all /г, h M M j∙
Observe that
AiM ≤ Аг|М1
= Аг(сМ + d)
— M Mt
= M(MjAcIMM)-
More intriguing information
1. The constitution and evolution of the stars2. Natural Resources: Curse or Blessing?
3. The name is absent
4. Income Taxation when Markets are Incomplete
5. Constrained School Choice
6. The name is absent
7. Innovation Policy and the Economy, Volume 11
8. The Role of Evidence in Establishing Trust in Repositories
9. The name is absent
10. Micro-strategies of Contextualization Cross-national Transfer of Socially Responsible Investment