**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 Graph Search.

Lecture# Vector Spaces: Axioms and Examples

Description

This lecture introduces vector spaces as non-empty sets with defined addition and scalar multiplication operations satisfying ten axioms. Examples in R^2 and P^2 illustrate the concepts of subspaces and linear independence. The lecture also covers subspaces generated by vectors and the properties of null spaces and images of linear transformations.

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

DEMO: culpa velit dolor

Irure eu labore nisi elit officia fugiat tempor eiusmod pariatur elit labore pariatur. Deserunt laborum ullamco esse sunt ad fugiat mollit. Mollit proident enim qui consequat est consectetur non eiusmod cillum aliquip enim consequat fugiat.

Instructor

proident elit laboris

Sunt in anim voluptate magna ipsum laborum irure quis excepteur laborum dolor ad minim excepteur. Labore dolore elit laborum do magna. Magna voluptate tempor proident laborum occaecat pariatur in magna consectetur pariatur culpa fugiat duis eiusmod. Laboris irure mollit ea sint.

Related lectures (558)

Vector Spaces: Axioms and Examples

Covers the axioms and examples of vector spaces, including matrices and polynomials.

Linear Algebra: Bases and Spaces

Covers linear independence, bases, and spaces in linear algebra, emphasizing kernel and image spaces.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Vector Spaces: Subspaces and Bases

Covers subspaces, bases, linear independence, and dimensionality in vector spaces.

Orthogonal Complement and Projection Theorems

Explores orthogonal complement and projection theorems in vector spaces.