What is eigenvector?

A eigenvector is like a special direction that doesn’t change when something gets stretched or squished, just like how your favorite toy might not rotate if you spin it the right way.

Imagine you have a rubber sheet, and you push on it from the sides. Most parts of the sheet will move in all directions, but some lines on the sheet stay straight, they just get longer or shorter. Those are the eigenvectors!

Think about playing with a square piece of clay. If you press it from the top and bottom, it gets taller, but if you press it from the sides, it gets wider. Now imagine pressing it in a special way that makes it stretch evenly along one line, that’s like an eigenvector! No matter how much you push or pull, that line stays aligned with itself.

It's like when you're on a swing and you move back and forth in the same direction every time. You’re going along the eigenvector of the swing, it’s the easiest way to go, and you don’t twist or turn anywhere else!