What's a Linear Isomorphism?

A linear map T is called an isomorphism if the following two conditions are satisfied. T is one to one. That is, if T(→x)=T(→y), then →x=→y. T is onto. That is, if → w ∈ W , there exists → v ∈ V such that T ( → v ) = → w .

How do you prove linear isomorphism?

A linear transformation T :V → W is called an isomorphism if it is both onto and one-to-one. The vector spaces V and W are said to be isomorphic if there exists an isomorphism T :V → W, and we write V ∼= W when this is the case.

What does isomorphism mean in linear algebra?

An isomorphism is a homomorphism that can be reversed; that is, an invertible homomorphism. So a vector space isomorphism is an invertible linear transformation.