Reductive group

Imagine a big group of toys, like all of your Lego pieces or all of your stuffed animals. Now imagine you want to group these toys together based on similarities they share. You might group all of the red Legos together, or all of the big stuffed animals together.

A reductive group is kind of like one of these toy groups, but for mathematical objects called matrices. Matrices are a lot like Lego pieces, but instead of being made out of plastic, they're made out of numbers.

To make a reductive group, mathematicians group matrices together based on similarities they share. These similarities have to do with the way the matrices transform other mathematical objects. Think of it like the way you might group all of your Legos that can build a certain type of structure together, or all of your stuffed animals that are good for cuddling together.

The big difference between a toy group and a reductive group is that a reductive group is made up of matrices, which are used to study all kinds of math problems. For example, reductive groups can help understand how to solve equations with more than one variable, or how to describe the shape of geometric objects. So even though they might seem like just a bunch of numbers, reductive groups can be really helpful for solving all sorts of important math problems!