Mr. Integral

THE BIG IDEA

Linear Transformations

Is the vector changing, or only the coordinates used to describe it?

A linear map transforms geometry consistently with addition and scaling. Separate that action from a change of basis, then use determinants to measure volume scaling and loss of invertibility.

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 with01Linear maps
  2. describing the same map differently uses02Coordinate changes
  3. measuring geometric scaling gives03Determinants

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. 01Linear Maps and GeometryRecognize a linear transformation and read its action from the images of basis vectors.
  2. 02Change of Basis and SimilarityTranslate coordinate descriptions and distinguish changing a vector from changing its coordinates.
  3. 03Determinants, Orientation and InvertibilityInterpret a determinant as signed volume scaling and compute it using row operations.