**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Low Rank Approximations

Description

This lecture covers the concept of low rank approximations, focusing on the mathematical theory behind it and its applications. The instructor explains the process of finding the best approximation of a matrix by a low-rank matrix, emphasizing the importance of spectral theorems and orthogonality. Various demonstrations and examples are provided to illustrate the theory, including the minimization of certain functions. The lecture concludes with a discussion on the practical implications of low rank approximations in data analysis and signal processing.

Login to watch the video

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

Instructor

Related concepts (81)

MATH-115(a): Advanced linear algebra II

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux de ce sujet.

Related lectures (12)

A notebook interface or computational notebook is a virtual notebook environment used for literate programming, a method of writing computer programs. Some notebooks are WYSIWYG environments including executable calculations embedded in formatted documents; others separate calculations and text into separate sections. Notebooks share some goals and features with spreadsheets and word processors but go beyond their limited data models. Modular notebooks may connect to a variety of computational back ends, called "kernels".

In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m−3), at any point in a volume. Surface charge density (σ) is the quantity of charge per unit area, measured in coulombs per square meter (C⋅m−2), at any point on a surface charge distribution on a two dimensional surface.

Project Jupyter (ˈdʒuːpɪtər) is a project to develop open-source software, open standards, and services for interactive computing across multiple programming languages. It was spun off from IPython in 2014 by Fernando Pérez and Brian Granger. Project Jupyter's name is a reference to the three core programming languages supported by Jupyter, which are Julia, Python and R. Its name and logo are an homage to Galileo's discovery of the moons of Jupiter, as documented in notebooks attributed to Galileo.

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be positive or negative (commonly carried by protons and electrons respectively, by convention). Like charges repel each other and unlike charges attract each other. An object with no net charge is referred to as electrically neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

In mathematics, particularly linear algebra and functional analysis, a spectral theorem is a result about when a linear operator or matrix can be diagonalized (that is, represented as a diagonal matrix in some basis). This is extremely useful because computations involving a diagonalizable matrix can often be reduced to much simpler computations involving the corresponding diagonal matrix. The concept of diagonalization is relatively straightforward for operators on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional spaces.

Hermite Normal Form

Covers the Hermite Normal Form, a method to transform a matrix into a specific form.

Linear Differential Equations

Covers the solution of linear differential equations, focusing on complex solutions and diagonalizable matrices.

Integer Cones

Covers the concept of integer cones and Carathéodory's theorem with illustrative examples.

Linear Algebra: Integers

Explores linear algebra over integers, emphasizing solutions to A.x=b equations and Hermite normal form.

Matrix Exponential and Jordan Normal Form

Covers the matrix exponential, its convergence properties, and the Jordan normal form.