Blogs
Series: The different ways we understand rotations
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.
The Kronecker Product
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.
Three interpretations of matrix products visualized
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.
Permutation matrices - from shuffle to symmetry
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.
Inverse of a block of a matrix
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.
Two ways to calculate the isometric projection matrix
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.
Inverse of a matrix after row and column removal
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.
Playground for matrix transformations
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.
Image quality assessment with CLIP projection matrices
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.