Linear subspace

Imagine you have a huge room and you want to draw a line in the middle of the floor. That line is a straight path that you can walk along without stepping off of it.

Now, let's say instead of just one line, you want to draw a bunch of lines in the room. Each line is still a straight path, but they might go in different directions or be different lengths.

If you think of each line as a "subspace" of the room, you could say that the whole room is made up of different subspaces (the individual lines). And if all of these lines go through the same point, like the middle of the room, then you could say that this point is a "linear subspace."

Basically, a linear subspace is a type of space that is made up of lines that go in different directions and can be different lengths, but all go through the same point. It's like a big collection of different lines that share something in common.