Series: Deep dives into specific topics
All about rotations
Rotation is linear
2D rotations
3D rotation matrices
Quaternions
Rotations as reflections
Geometric algebra
Lie algebra
This series starts from 2D rotation matrices and takes us through the developments we have made to understand and describe rotations - it covers imaginary numbers, intrinsic and extrinsic rotations, Euler angles, quaternions, geometric algebra and Lie theory.
Matrix calculus and autodiff
Linear operator
Gradient of a function
Jacobian of a function
Key matrix derivatives
Function is a DAG
Autodiff on a DAG
VJP and JVP
Hessian of a function
Starting from the idea of a small change in output given a small change in input, this series builds the concepts of linear operators, gradients and Jacobians, and covers the foundational ideas behind autodiff alongwith links to implementations in PyTorch and JAX.