Lecture

Vector Spaces and Linear Applications

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. It covers examples of vector spaces with usual addition and scalar multiplication in R^2, matrices, and polynomials. The concept of subspaces is explained, along with the properties of subspaces and their verification. The lecture also discusses the kernel and image of a matrix, as well as the reduced row-echelon form and solutions of linear systems. It concludes with the concepts of linear independence, bases, and the differences between the kernel and image of a matrix.

Instructor

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Official source

https://mediaspace.epfl.ch/media/0_l3ig3l45

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Analysis: Numerical analysis, Functional analysis

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