Web Reference: Here an isomorphism just a bijective linear map between linear spaces. Two linear spaces are isomorphic if there exists a linear isomorphism between them. Aug 4, 2021 · An isomorphism picks out certain traits of one object, certain traits of the other, and shows that the two objects are the same in that specific way. Two sets are "isomorphic" when there is a $1-1$ mapping between them, so in this case isomorphism means having the same cardinality--the same number of elements. Nov 28, 2015 · For sets: isomorphic means same cardinality, so cardinality is the "classifier". For vector spaces: isomorphic means same dimension, so dimension (i.e., cardinality of a base) is our classifier. I is a bit more complex but still not too difficult (you'll probably encounter it in your book sooner or later) to classify finite abelian groups.
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Last Updated: April 15, 2026
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