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Definition LT. Linear Transformation. A linear transformation, T : U â V , is a function that carries elements of the vector space U (called the domain) to the vector space V (called the codomain), and which has two additional properties.
Proof that a linear transformation is isomorphic. up vote 1 down vote favorite. As a homework, i need to proove whether a few linear transformations are isomorphic or not, however i do not know how to achieve this. First of all i have proven that the following map is linear: $$f:\mathbb{R}^2\mapsto\mathbb{R}^2, ....y the definition the linear isomorphism is a linear bijective map. We should show that for any point $(x,y)\in \mathbb R^2$ there exists unique point $(x',y')\in \mathbb R^2$ such that $f(x',y') = (x,y)$ (this point is called pre-image of $(x,y)$). Note that these any + unique are properties of a bijection.