References: Stepping up to 3D

Source material

Source curriculum (structural mirror, cited as further study):
• 3Blue1Brown, Essence of Linear Algebra, Chapter 5: "Three-dimensional linear transformations"
  Creator: Grant Sanderson
  Lesson page: https://www.3blue1brown.com/lessons/3d-transformations
  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

• Three-dimensional linear transformations (3Blue1Brown) by Grant Sanderson. The video this lesson mirrors. Seeing a 3D grid rotate and the unit cube shear into a slanted box in motion does more for 3D intuition than any still picture can. Short, and the visual payoff is high. Watch it right after this lesson.

Going deeper

• Essence of Linear Algebra (full series) by 3Blue1Brown. The series this track follows. The previous chapters built the 2D machinery this lesson lifts into 3D; the next (The determinant) asks by how much a transformation stretches or squashes the space it acts on.

• Khan Academy: Linear algebra for a slower, exercise-driven treatment, with practice problems and immediate feedback on transformations and matrices.

Adjacent topics

Where this sits in the track.

• Matrix multiplication as composition (previous lesson). Composition works identically in 3D: each column of AB is A applied to that column of B, just with 3-vector columns. If 3D feels like more of the same, that is the intended takeaway.

• The determinant (next lesson). Once you can picture a transformation reshaping the unit cube, the natural question is how much it changed the cube’s volume. That single number, positive, negative, or zero, is the determinant, and it works the same way for the area of the unit square in 2D.