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  • Isomorphism

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  • Every finite dimensional vector space over R (or C) is isomorphic to R^n (or C^n) for some n.
  • 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
  • Definition of automorphism of a vector space
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  1. Definition of isomorphic/isomorphism between vector spaces

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  • IsomorphismClose match
  • Vector space isomorphism is an equivalence relation.Close match
  • Finite-dimensional vector spaces of equal dimension over the same field are isomorphicClose match
  • Isomorphic vector spaces have the same dimension.Close match
  • Every finite dimensional vector space over R (or C) is isomorphic to R^n (or C^n) for some n.Close match
  • Definition of automorphism of a vector spaceClose match
  • Abstract vector spacesClose match
  • Definition and terminologyClose match
  • The inverse of an isomorphism is an isomorphism.Close match
  • Axioms of a vector spaceClose match
  • Vector spacesClose match
  • Coordinate vector spacesClose match
  • Equivalence theorems for injective transformationsClose match
  • Definition of vector additionRelated
  • Definition of linear combination of vectorsRelated
  • Definition of a vector being orthogonal to a subspaceRelated
  • Definition of parallel vectorsRelated
  • A vector can be written uniquely as a linear combination of vectors from independent subspaces.Related
  • Definition of inner product spaceRelated
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