A question on convex sets

Question

The definition I’ve been given of convex inequalities is the following:
A set A ⊂ Rn is convex if:
• For any vectors a, b ∈ A
• For any λ ∈ [0,1]
• The point λa + (1 - λ)b ∈ A

I don’t know what the λ stands for it means. Could someone please explain it to me and put it in context to the definition?

Answer 1

λ is scalar between 0 and 1. Now if you change λ in λa + (1 - λ)b from 0 to 1 you move from b to a (or it could be written other way around from a to b).

A convex set is a set, where any two elements can be connected by a straight line. To make easier understanding think of a set of two-dimensional vectors and connect any two points, elements or vectors (if you wish).

I hope it helps.

[In case of one dimension, if you look at the expression y=λu+(1-λ)v, and λ change from 1 to 0, y changes from u to v ].