Let V be a vector space with basis , and let be the linear transformation . Then T is an isomorphism, and the matrix of T with respect to G and the standard basis is the identity matrix.

Question

Let V be a vector space with basis  , and let  be the linear transformation  . Then T is an isomorphism, and the matrix of T with respect to G and the standard basis is the  identity matrix.​

Quizplus · Accepted Answer

By definition, an isomorphism is a bijective linear transformation. Since the basis of the vector space V and the standard basis are related by the identity matrix, and the linear transformation T is bijective, we can conclude that T is an isomorphism.

Let V Be a Vector Space with Basis