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Lecture
Vector Spaces: Bases and Dimensions
Description
This lecture covers the concept of bases in vector spaces, including the representation theorem for vectors in a base, the uniqueness of bases, and the dimension of vector spaces. It also explores examples of bases, dimensions of subspaces, and the isomorphism between vector spaces. The lecture concludes with practical facts about completing bases and the relationship between the dimension of subspaces and the dimension of the whole space.
Official source
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