Positive-definite function on a group
When we talk about a function on a group, it’s like a special machine that takes something from the group as an input and gives a number as an output. Think of it like a vending machine – you put in a certain coin (group element), and it gives you a candy bar (number).
A positive-definite function on a group is a special kind of function that always gives us positive numbers as its outputs. It’s like a vending machine that never gives sour candy, always something sweet!
But, just like how we have to put in the right coin for a vending machine to work, we have to make sure we’re putting in the right kind of things into our positive-definite function for it to work properly. Specifically, we need to make sure whatever we’re putting in is a group element that’s not “zero” (meaning it’s not the identity element), or else our function won’t work.
So, in summary, a positive-definite function on a group is a special machine that takes something from the group and gives us back a positive number, but we have to make sure we’re putting in the right things to get the best results!
A positive-definite function on a group is a special kind of function that always gives us positive numbers as its outputs. It’s like a vending machine that never gives sour candy, always something sweet!
But, just like how we have to put in the right coin for a vending machine to work, we have to make sure we’re putting in the right kind of things into our positive-definite function for it to work properly. Specifically, we need to make sure whatever we’re putting in is a group element that’s not “zero” (meaning it’s not the identity element), or else our function won’t work.
So, in summary, a positive-definite function on a group is a special machine that takes something from the group and gives us back a positive number, but we have to make sure we’re putting in the right things to get the best results!