Vector Spaces: Axioms and Examples

In course

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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.

Instructor

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Official source

https://mediaspace.epfl.ch/media/0_0tgbd4om

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra, Abstract algebra

Analysis: Functional analysis, Tensor analysis

Linguistics

Theoretical linguistics: Syntax

Logic

Classical logic: First-order logic

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