Lesson 5.1 · 18 of 25 lessons
Eigenvectors
Start with directions preserved by a transform and see how diagonalization simplifies the action.
Open the interactive animation01 · Story
What to verify in this scene
Follow the explanations and operations, then identify the mathematical evidence that remains in the final scene.
- 01
e keeps its direction through D, while q changes direction
- 02
Apply D and compare the direction of the two vectors
- 03
e stayed on the same line and only doubled in length
A vector whose direction is preserved is an eigenvector
02 · Notebook
The runnable notebook
This source creates the mathematical objects and controls the order of operations and animation. Read it here, then play the same scene yourself.
2d
zoom 9/10
grid off
relative-grid on
coordinates on
2 0 #D
0 1
1, 0 #e@
1, 1 #q@
// {{e}} keeps its direction through {{D}}, while {{q}} changes direction
focus e q
checkpoint Eigenvectors
focus -
// Apply {{D}} and compare the direction of the two vectors
D
// {{e}} stayed on the same line and only doubled in length\nA vector whose direction is preserved is an **eigenvector**
focus e03 · Unit 5
Lessons in this unit
Eigenvalues & eigenvectors — Start with directions preserved by a transform and see how diagonalization simplifies the action.