So I thought I understood well enough what a Jacobian was (in the context of an $n$-DOF robot) -- a function that takes a vector of n joint positions and returns an $n \times n$ matrix that can be multiplied with a vector of $n$ joint velocities to return a velocity vector for the end effector.
I'm using ROS and MoveIt, so I actually already have a function to calculate the Jacobian for my robot from the URDF.
However, I'm reading lecture notes from the 2005 MIT Intro to Robotics course, and in one (mission-critical, it seems) portion of chapter 7 (between pages 11 and 12), he refers to "$3 \times n$ Jacobian matrices relating the centroid linear velocity and the angular velocity of the $i^\text{th}$ link to joint" as $J^L$ and $J^A$.
He introduces Jacobians in Chapter 5, and indeed I looked through all the rest of the course material, and I don't think he ever explains what these matrices are or how to compute them.
Could someone enlighten me as to what he's talking about?