Positive definite function on a group

Okay kiddo, so imagine you and your friends are playing a game together. In order to play the game, you all have to follow some rules. These rules are like a set of instructions that tell you what you can and cannot do.

Now, imagine that these rules can be compared to something called a "group". A group is just a fancy way of saying that there are rules that everyone has to follow when they are playing together.

But different groups might have different rules, right? And in some groups, it might be easier to play together than in others. That's where something called a "positive definite function" comes in.

A positive definite function is like a measure of how easy it is to play nicely together in a group. It tells you if everyone is following the rules and playing nicely or if someone is being mean and breaking the rules.

If the positive definite function is high, that means everyone is playing nicely and following the rules. But if the positive definite function is low, that means someone might be causing trouble and not following the rules.

So, to sum it up, a positive definite function is a way of measuring how well a group is working together and following the rules of the game.