Vector Inequalities

Question

If x, y are vectors in Rⁿ, prove that

| ||x|| - ||y|| | <= || x-y ||

Answer 1

this is called inverse triangle inequality.

x=x-y+y

||x||=||x-y+y||

||x||=||x-y+y||≤||x-y||+||y|| ,,,,is triangle inequality

||x||-||y||≤||x-y||

found on web