Math

Computations on Hyperbolic Geometry

Note on Hyperbolic Geometry Reference Notes 2018 Lec Note 2015 Lecture note Ch5-3 Measurement in Hyperbolic Geometry [Cheatsheet / Note](http://home.iiserb.ac.in/~kashyap/MTH 520/lp.pdf) Motivation Hyperbolic geometry is a great source of inspiration for math art. Besides it is used to model some hierarchical data structure. Here I collected a few models

Apr 10, 2020

Note on Epipolar Geometry and Optic Slow

Motivation This is a brief analytical note about how physical self movement of eye / camera will induce optic flow in a static environment. And then discuss how a system can separate these two components instantaneously.

Feb 17, 2020

Krylov Subspace, Conjugate Gradient and Lancosz Iteration

Krylov Subspace, Lancosz Iteration, QR and Conjugate Gradient Motivation In practise, many numerical algorithms include iteratively multiply a matrix, like power method and QR algorithm. All these algorithms have their core connected to a single construct, Krylov subspace and a operation, Lancosz Iteration. So this note motivates to understand this core.

Jan 1, 2020

Some Computation on Sphere

Some Computation on Sphere (Updating) Motivation Recently, in research, we encounter quite a few statistical problems on sphere. For example, Head direction tuning 3d direction of object 3d direction of body parts Some 3d tuning There are many standard statistical operations on Euclidean space, like getting mean, standard deviation and generate uniform distribution, fitting a model etc. We can perform these operation without thinking.

Oct 13, 2019