Mathematics articles
In this article, we will see how the Legendre transform is a clever way of encoding the information carried by a function F(x) into another function G(s) which might be easier to deal with. We’ll provide some geometrical intuition and give some examples at the end to use this tool in practice.
In this article we will see how every multivariate Gaussian can be thought as the product of n one dimensional Gaussian distributions followed by a linear transformation and how it can be used to represent correlated Gaussian data.
There are two types of line integrals: line integrals of scalar fields and vector fields. In this article we will see how the first type evaluates the area under a function delimited by a curve gammva, while the second type evaluates the work of a vector field on a specific trajectory.
In this article we are going to derive the Bayes formula using basic tools in probability theory and see how it can be viewed as a tool for updating probabilities based on new evidence, providing two examples to fully understand it.
In this article we will define Maximum Likelihood estimation as a general framework for distribution inference from data and apply it to several kinds of data distributions. This method can be used to determine the optimal loss function to be used when training a neural network on experimental data.
In this article we will define what a group is abstractly and provide several examples to have a feeling for what the abstract definition really means. We will then define some general elements in group theory and focus on the idea of group generators.
In this article we will define Lie groups and their relationship with Lie algebras and show how these are effective tools for the representation of Lie groups by means of infinitesimal generators geared with a commutation rule, namely Lie brackets.
In this article we are going to define the idea of Nash equilibrium in game theory as the stable situation in which every player has no incentive to change their game and show how this can be used to find the optimal strategy in non-cooperative games.