Eigenvalues and eigenvectors

What you'll learn

1. 1

   Imagine a rubber sheet stretched in a frame. If you push on it in a certain direction, some points only stretch along that line — they don't twist sideways.

2. 2

   What does an eigenvector do when you apply a transformation?

3. 3

   Here's a 2D grid. The red arrow is an eigenvector — after the transformation (shown in blue), it still points the same direction, just longer.

4. 4

   Let's find eigenvalues and eigenvectors of matrix A = [[2, 0], [0, 3]].

5. 5

   Drag the eigenvector arrow to see how it stretches under this transformation.

6. 6

   For matrix [[3, 0], [0, 4]], what is one eigenvalue?

7. 7

   True or false: Every vector is an eigenvector of some transformation.