Projective unitary group

Imagine you and your friends have a big playground with a lot of toys like swings, slides, and monkey bars. Now imagine that, instead of playing on the equipment, you want to play a game where you move the equipment around in different positions.

To keep the game fair, you agree that each time you move the equipment, you have to do it in a way that keeps the distances and angles between them the same as they were before. This way, no one can cheat by moving everything too close or too far apart.

The projective unitary group is kind of like this game. Instead of moving playground equipment, it deals with the way shapes and objects move around in space, while keeping certain distances and angles. However, in the projective unitary group, the shapes and objects are represented by numbers, and the distances and angles are represented by mathematical equations.

So, the projective unitary group is a fancy way of describing how numbers can be transformed while keeping certain mathematical relationships the same. Just like how you and your friends move the playground equipment in your game while keeping everything fair and equal.