pseudoinverse

When there's no exact solution, project. When data is high-dimensional, compress. The SVD is the Swiss Army knife that does both — and more. Master orthogonal projection, the normal equations, the Singular Value Decomposition, low-rank approximation, and the pseudoinverse.

Connect joint velocities to end-effector velocity through the Jacobian matrix. Learn how to build J, spot singularities where det J = 0, invert J with the pseudoinverse for velocity control, and measure manipulability — with NumPy code for the 2-link arm.