A model of computation is a theoretical framework that abstracts the essential features of a computing system, allowing us to analyze and compare different algorithms and machines based on their computational power and efficiency. In computer science, models of computation are used to study the limits and possibilities of computation, and to explore the relationships between different computational problems and their solutions. By formalizing the notion of computation, models of computation have become essential tools for theoretical computer scientists, algorithm designers, and anyone interested in understanding the nature and scope of computation.

During my preparatory classes worked on a project that I presented at the oral examination. It was one of my first encounter with the world of research in mathematics. I worked on an extremely interesting subject that I did not even suspect existed. The goal of the project was to hide information into an image and being able to decode it. The principle behind this process is called steganography. Steganography Definition Steganography is the practice of concealing a message within another message or a physical object.

There are different technique to reduce dimensionality. One of the most known is Principal Component Analysis (PCA). Probably the most known one. The aim of this article is to explain the math behind PCA. It is based on eigen decomposition. Figure 1 : PCA" Figure 1 : PCA PCA is based on the properties of symmetric matrices and eigen decomposition. Let’s consider the set of vectors { \( x_1,…,x_n \) } that represent our data.