jacobian
4 free lessons tagged jacobian across Math, Robotics. Each one is a short sequence of focused steps with narration and a five-question quiz at the end — take them in any order, no signup required.
The Chain Rule, and Why Depth Is Hard
A deep network is a composition, so its derivative is a product of Jacobians. This lesson builds the chain rule from one variable up to matrix form, shows that the order you multiply that product in changes the cost tenfold, and explains vanishing gradients as an arithmetic consequence rather than a mystery.
Gradients, Jacobians, and Hessians: Calculus in Many Dimensions
One derivative becomes three objects once a function has many inputs and many outputs. This lesson builds the gradient, the Jacobian and the Hessian, shows what each one actually tells you, and explains why curvature decides how many steps an optimiser needs and why nobody ever writes the Hessian down.
The Jacobian and Velocity Kinematics
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.
Inverse Kinematics: From Pose to Joint Angles
Flip the FK problem: given a desired end-effector pose, find the joint angles that achieve it. Master analytical closed-form IK for the 2-link arm, the elbow-up/elbow-down duality, atan2 arithmetic, and the basics of numerical IK via the Jacobian.