subspaces

Vectors are more than arrows — they're the atoms of every ML model, physics engine, and signal processor alive. Build rock-solid intuition for linear combinations, span, independence, basis, and orthogonality, then verify it all in NumPy.

A matrix doesn't just hold numbers — it reshapes space. Master the geometric view of matrix-vector multiplication, the four fundamental subspaces, rank, the determinant as a volume-scaling factor, and invertibility — all grounded in NumPy.