References: Matrix multiplication as composition

Source material

Source curriculum (structural mirror, cited as further study):
• 3Blue1Brown, Essence of Linear Algebra, Chapter 4: "Matrix multiplication as composition"
  Creator: Grant Sanderson
  Lesson page: https://www.3blue1brown.com/lessons/matrix-multiplication
  Series index: https://www.3blue1brown.com/?topic=linear-algebra
  License: copyright Grant Sanderson; videos published on his site and YouTube
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Watch this next

• Matrix multiplication as composition (3Blue1Brown) by Grant Sanderson. The video this lesson mirrors. Watching the grid get rotated and then sheared, with the two matrices visibly chaining right to left, is what makes “multiplication is composition” stick. The non-commutativity demonstration (the same two moves in opposite orders landing on different grids) is especially worth seeing animated. About ten minutes.

Going deeper

• Essence of Linear Algebra (full series) by 3Blue1Brown. The series this track follows. The previous chapter (linear transformations and matrices) defines the single-matrix idea this lesson chains; the next (Three-dimensional linear transformations) carries everything up into 3D.

• Khan Academy: Linear algebra for a slower, exercise-driven treatment. The matrix-multiplication material there gives you problems to practice the mechanics, with immediate feedback.

Adjacent topics

Where this sits in the track.

• Linear transformations as moves (previous lesson). This lesson chains the single transformations from the previous one. If “apply A to each column of B” felt fast, it is just the previous lesson’s matrix-vector product run once per column, so a quick reread grounds it.

• Three-dimensional linear transformations (next lesson). Everything so far lives in the flat plane. The next lesson keeps every rule identical (matrix is where the basis lands, multiplication is composition) and adds a third basis vector and a third dimension, so a transformation becomes a 3-by-3 matrix.