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. 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. Aug 4, 2021 · An isomorphism is a particular type of map, and we often use the symbol $\cong$ to denote that two objects are isomorphic to one another. Two objects are isomorphic there is a $1$ - $1$ map from one object onto the other that preserves all of the structure that we're studying. That second part is important, but it's often implied from context.
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