Lesson 29 of 48
Matrices as transformations
A matrix is not a grid of numbers. It is something that happens to space.
Seeing a matrix as an action — stretch, rotate, shear, collapse — makes every later matrix fact feel inevitable instead of memorised. A network layer is exactly one of these actions plus a bend.
Do this
Apply a 2×2 matrix by hand to the four corners of the unit square and draw the result. Verify with code. Then construct a matrix that produces a transformation you chose in advance.
The question that unlocks the next lesson
What do the columns of a 2×2 matrix tell you directly?
- AIts determinant
- BWhere the basis vectors (1,0) and (0,1) land after the transformation
- CIts eigenvalues
- DThe angle of rotation, always