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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.
Vector spaces with the same dimension are isomprphic.
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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Isomorphism
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The inverse of an isomorphism is an isomorphism.
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