I want to show that if $$(u-\hat u, v-\hat u)\leq 0$$ and also $$(v-\hat v, u-\hat v)\leq 0$$ then $$(\hat u-\hat v, u-v)\geq 0$$
Please help me. Maybe it is easy
Thanks
2026-04-25 13:59:15.1777125555
inequality in inner product
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Hint: Euler identity
$$(u-\hat u, v-\hat u)- (v-\hat v, u-\hat v)+ (\hat u-\hat v, u-v)= 0.$$
(So I suppose you've made a typo)