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  • Abstract vector spaces

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  • Linear (in)dependence
  • Bases
  • Linear transformations
  • Definition and terminology
  • Linear combinations
  • Subspaces
  • Basic properties
  • Isomorphism
  • Orthogonality and projection

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  • Definition of isomorphic/isomorphism between vector spaces
  • The inverse of an isomorphism is an isomorphism.
  • Vector space isomorphism is an equivalence relation.
  • Isomorphic vector spaces have the same dimension.
  • Finite-dimensional vector spaces of equal dimension over the same field are isomorphic
  • Every finite dimensional vector space over R (or C) is isomorphic to R^n (or C^n) for some n.
  • Definition of automorphism of a vector space
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  1. Isomorphism

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