Linear algebra

Robotics linear algebra is mostly “matrices move vectors” and “some matrices are rotations.” A rotation \(R\) satisfies \(R^\top R=I\) and \(\det R=1\). Columns are the body axes written in the world. Homogeneous \(T\) adds a translation so you can concatenate \(T_{WA}T_{AB}=T_{WB}\).

Jacobians are just stacked derivatives. Rank tells you whether a direction is lost (singular IK, unobservable estimator). Eigenvectors of a covariance point along the error-ellipse axes; eigenvalues are the variances in those directions. If those four sentences are solid, you can survive the book’s mechanism and uncertainty parts.