given 𝑛 points 𝑥₁, 𝑥₂, …, 𝑥_𝑛 ∈ 𝑋 we call any point 𝑦 a convex combination of those 𝑛 points iff:

• 𝑦 = 𝛴_{1≤𝑖≤𝑛} [𝜆_𝑖𝑥_𝑖]

where:

• 𝜆₁, 𝜆₂, …, 𝜆_𝑛 ≥ 0
• 𝛴_{1≤𝑖≤𝑛} [𝜆_𝑖] = 1

Intuition

https://math.stackexchange.com/questions/2365788/convex-combination-meaning