What Are Eigenvalues and Eigenvectors?

Eigenvalues and eigenvectors are important ideas in math, especially when we talk about changing shapes and sizes!

• Eigenvalues ($\lambda$): These are numbers that show how much we stretch or shrink an eigenvector.

• Eigenvectors ($\mathbf{v}$): These are special arrows that don't point in a different direction when we apply a change; they just get longer or shorter.

Why Are They Important?

1. They make complex changes easier to understand.
2. They help us see important features of linear systems.
3. They're useful in real life for things like studying how things move or stay steady!

Embrace the power of linear algebra with these cool ideas! 🎉