Convex combination

When we talk about a convex combination, we are basically talking about mixing things together. You know how when you mix two colors of paint together, you get a new color? That's sort of like what a convex combination is.

But instead of paint, we're talking about numbers. Let's say you have two numbers, x and y. If you want to find a convex combination of x and y, you need to pick two other numbers, a and b, that add up to 1. So a + b = 1.

Then, you take x and multiply it by a, and you take y and multiply it by b. Finally, you add those two things together. The result is a convex combination of x and y.

But why do we care about convex combinations? Well, they come up a lot in math and science when we're trying to find the "average" of things. For example, if you want to find the average color of two paints, you might use a convex combination. Or if you want to find the center of mass of an object, you might use a convex combination of the masses of its parts.

So remember: a convex combination is like mixing two numbers together using two other numbers that add up to 1. It's a way of finding averages and centers.