Lecture

Manifolds and Tangent Space

Description

This lecture covers the concept of manifolds, which are spaces that locally resemble Euclidean space, and introduces the idea of charts and atlases to describe manifolds. It also explains the tangent space as the space of tangent vectors to curves on a manifold, and discusses the change of coordinates and basis in vector spaces. Additionally, the lecture delves into tensors as linear maps and the metric, which defines the line element in a manifold. The instructor provides insights on how to define lengths and distances in a curved space.

About this result
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.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.