I am a bit confused about the proof of the convexity of the norm. Suppose I consider 1 norm form in which case the function is $f(x) = ||x||_1$
Referring to this pdf, http://ttic.uchicago.edu/~argyriou/courses/lec3.pdf. They have given something like
I didn't get this proof. How come they consider it a triangle? I mean $\lambda w$ and $(1-\lambda)z$ are just points so how come the triangular equality came into. I think I am finding it difficult to visualize. Can anyone suggest something?