Inverse of vector space isomorphism is also linear ↩

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created: 2021-11-06 14:48:37
modified: 2022-01-10 04:13:04

Statement:
If

is a linear map which is an isomorphism, then

is also a linear map (and thus is also an isomorphism).

Proof

Let and . Since is one-to-one, such that , . Then so that

This shows the linearity of .