Mr. Integral

THE BIG IDEA

SVD and Engineering Computation

Which parts of a matrix carry the strongest signal?

Singular values describe stretching even when a matrix is rectangular or lacks an eigenbasis. Use those stretches to build approximations and diagnose why small measurement errors can produce large solution errors.

Begin the first lesson →See the lesson route ↓

3 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Singular directions
  2. comparing stretches explains02Sensitivity & low rank
  3. combining the tools supports03Choosing a method

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit3 lessons
  1. 01Singular Value DecompositionDescribe any rectangular matrix using orthogonal directions and nonnegative stretches.
  2. 02Pseudoinverses, Low Rank and ConditioningUse singular values to solve least-squares problems and understand sensitivity to noisy data.
  3. 03Linear Algebra CheckpointConnect systems, spaces, projections and spectral methods in a single set of problems.