Series: Deep dives into specific topics

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.

From Permutations to Sinkhorn

Overview and permutation cycles Permutation spectra Circulant matrices Birkhoff polytope Doubly stochastic matrices Birkhoff-von-Neumann algorithm Matrix scaling Sinkhorn distance

Explore the journey from the spectral properties of permutations to the geometry of doubly stochastic matrices, Birkhoff’s polytope, and how it all leads to Sinkhorn distances in optimization and machine learning.