Abstract vector spaces | Essence of linear algebra, chapter 15

The video explores the concept of vectors, questioning their fundamental nature and discussing their representation as arrows or lists of numbers. It extends the idea of vectors to functions, highlighting their vector-like properties such as addition and scaling. The video delves into linear transformations, emphasizing their properties of additivity and scaling, and explains how derivatives can be represented using matrices in function spaces. It concludes with a discussion on abstract vector spaces, introducing axioms that define them and emphasizing the general applicability of linear algebra concepts.

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