Question

Hello

I'm not an english speaker, so sorry for my bad english.

I've got problem with the triangle inequality for norms. When there is = ?

Answer 1

That's okay; most english speakers have poor english, too! :)

Answer 2

Do you mean, what happens when 2 sides of a triangle together equal the third?

Answer 3

@geoffb - so true!

Answer 4

i mean when the norm of x + y is equal to norm of x + norm of y

Answer 5

Can you define 'norm' for me, please?

Answer 6

ok wait a second

Answer 7

I think you're referring to the lengths/magnitudes, yes? I just want to be sure.

Answer 8

i.e. norm of x + y = |x + y| ?

Answer 9

yeah

Answer 10

its a lenght of vector

Answer 11

In that case, the triangle would collapse. Imagine actually trying to build a triangle out of three pieces of wood -

Answer 12

For a triangle, a + b > c, a + c > b, b + c > a.

Answer 13

could you show it in more general?