This series on rotations starts from 2D rotation matrices and takes us through the developments we have made to understand and describe rotations - it covers topics of imaginary numbers, quaternions, geometric algebra and Lie theory.

Kronecker product is a way to multiply two matrices of any shape. This apparently simple product has a lot of desirable properties and finds applications in different areas.

This article revisits the building blocks of linear algebra - matrix-vector and matrix-matrix products. It provides animations to quickly grasp the different ways to interpret these products. It also talks about scenarios where each interpretation is useful.

Essentially born from shuffling the rows or columns of an identity matrix, these matrices carry a distinctive set of properties that make them valuable in various mathematical applications. This article explores some of their fundamental properties and applications in various fields.

This is a further generalization of the problem of calculating the inverse of a matrix after removing a row and a column. But what about removing k-rows and k-columns? Exploring this problem also leads us to a well known matrix - the Schur Complement.

We explore two methods to derive the isometric projection matrix. The first one involves two rotations of a unit cube. The second one is a first principles approach to arrive at the solution without any rotation.

How is the inverse of a matrix related to the inverse of the matrix with a specific row and column removed? I encountered this problem while reading a paper on post-training quantization. This article digs deeper into the original problem and some of its variants.

Type (almost) whatever you want to visualize in plain English - you can add vectors, polygons, points on a circle. You can rotate the input vectors or the transformation matrix.

A neat little trick to assess image quality using CLIP. Roughly speaking, an image assessment model gives a score to an image based on its quality, aesthetics etc. While there are specifically trained models for this, we can also achieve this functionality using a multi-modal model like CLIP.