References: Linear transformations as moves

Source material

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

• Linear transformations and matrices (3Blue1Brown) by Grant Sanderson. The video this lesson mirrors. Watching the grid stretch and rotate while the basis vectors drag everything with them is the single fastest way to make “a matrix is where the basis lands” feel obvious. About eleven minutes. The animation of the unit square turning into a parallelogram is worth the watch on its own.

Going deeper

• Essence of Linear Algebra (full series) by 3Blue1Brown. The series this track follows. The previous chapter (spans and basis) sets up the basis-vector idea this lesson leans on; the next (Matrix multiplication as composition) shows what happens when you chain two transformations.

• Khan Academy: Linear algebra for a slower, exercise-driven treatment. The “Matrix transformations” unit covers exactly this lesson’s ground, with practice problems and immediate feedback.

Adjacent topics

Where this sits in the track.

• Spans and basis (previous lesson). This lesson is built on the basis idea: every vector is a combination of i-hat and j-hat, so following those two vectors is enough to follow them all. If the linearity-preserves-combinations step felt fast, a reread of the previous lesson grounds it.

• Matrix multiplication as composition (next lesson). If one matrix is one transformation, doing two transformations back to back is multiplying two matrices. The next lesson shows that matrix multiplication is not an arbitrary rule either; it is “do this move, then that move,” read right to left.