How Does Eigen values and Eigen vectors in 3 mins Work?

Imagine you're on a swing, when you push it just right, it keeps going higher and higher without much effort. That's like eigenvalues and eigen vectors in action!

You can think of the swing as something being pushed or pulled. When you add just the right amount of force at the right time, the swing moves in a smooth, repeating motion, that’s what an eigen vector is: the direction it naturally swings in.

Now imagine different ways to push the swing. Some pushes make it go higher quickly (that's like a bigger eigenvalue), while others might make it sway slowly (a smaller eigenvalue). Each eigenvalue tells you how much "power" or "speed" the direction has.

Imagine you have three swings, each with its own natural rhythm. When you push them all at once, they go in different directions and speeds, but if you know their eigenvalues and vectors, you can predict exactly how each one will move!

It’s like having a special map for each swing that tells you: “If I push this way, it'll do this.” That's the eigenvalue and eigen vector working together, helping you understand patterns in motion, just like in math! Imagine you're on a swing, when you push it just right, it keeps going higher and higher without much effort. That's like eigenvalues and eigen vectors in action!