To expand on some of the other replies: maybe not QR and Gauss-Jordan directly, but understanding linear maps and subspaces is relevant in kinematics, especiall

To expand on some of the other replies: maybe not QR and Gauss-Jordan directly, but understanding linear maps and subspaces is relevant in kinematics, especially kinematic chains like robot arms / manipulators. You can formulate a task in terms of some nonlinear function mapping the robot's joint positions to a desired "task space" and set a reference point or trajectory in that space (e.g. keep a tool perpendicular to a surface while following a line on that surface). Approaches for solving these tasks usually look at the Jacobian (inverse) of the task-function and use iterative methods to find a trajectory in joint-space that solves the task, either making a plan offline or as part of the control algorithm in real time. The singular value decomposition of that Jacobian has a couple of applications like - find the pseudoinverse for the solution - use the condition number to detect (proximity to) singularities - find a Tikhonov-regularized solution to avoid singularities (aka. "singularity robust inverse" or "damped least squares") - find a projection into the null space of the Jacobian or that of a lower-rank approximation and solve lower priority tasks in that space - use the range of the Jacobian to measure "manipulability" or agility in task space, e.g. as a secondary optimization objective