Maths 3.6Lesson outlineLesson 6 of 7 in Module 3
Singular Value Decomposition
Factor any matrix into rotate–stretch–rotate, and keep only the largest parts.
Video in production.
Learn
In this lesson11 parts
- 01A decomposition for any matrix
- 02The unit circle becomes an ellipse
- 03Rotate, stretch, rotate
- 04Reading the singular values
- 05Keeping the largest part
- 06Any shape of matrix
- 07Checkpoint: the S V D so far
- 08The digits' singular values
- 09Rebuilding the images from k directions
- 10The S V D in NumPy
- 11Recap, challenge, and next: the covariance matrix
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- singular value
- the length of a semi-axis of the ellipse; how much the matrix stretches one direction |
6.7082,2.2361 - singular vectors
vᵢ, the input directions, anduᵢ, where they land |v₁at 45°,u₁at 71.57°- SVD
A = UΣVᵀ: rotate, stretch along the axes, rotate | every matrix- low-rank approximation
- keep the
klargest singular values; the best possible approximation of rankk| digits,k = 21
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.