Grassmannian manifold

Okay kiddo, so you know what a space is, like the room you're in right now. Now imagine that this space has a lot of lines going through it, like the lines on a piece of graph paper.

Now imagine that you can only move in a certain way along these lines, like only going up and down or side to side, but not diagonally. This is kind of what a Grassmannian manifold is like - a space made up of lots of lines that you can only move along in certain ways.

But instead of just two dimensions like a piece of graph paper, a Grassmannian manifold can have lots of dimensions (like 3D, 4D, or even more).

And instead of just lines, these spaces are made up of things called subspaces, which are sort of like smaller spaces that are inside the bigger space.

So basically, a Grassmannian manifold is a space made up of lots of subspaces that you can move along in certain ways, and it can have lots of different dimensions depending on how many subspaces there are.