Lecture

Vector Spaces: Structure and Bases

Description

This lecture covers the structure of vector spaces, focusing on vectorial lines and planes in R³. It explains the concept of bases, decomposition of vectors, and canonical bases. The instructor demonstrates how to determine if vectors are proportional and how to find bases in R³ using matrices.

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.
Related lectures (153)
Matrix Representations of Linear Applications
Covers matrix representations of linear applications in R³ and the invariance of rank.
Linear Applications Overview
Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.
Vectors: Coordinate Calculations
Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.
Diagonalization of Linear Transformations
Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.
Vector Spaces in R2 and R3
Covers vector spaces in R2 and R3, including examples of proportional families and coordinate transformations.
Show more

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.