Topics: Algebra - Linear Transformation - Vector Space

When a linear transformation is bijective, we call it an isomorphism.

We say that and are isomorphic if there exists a between them that’s an isomorphism. We denote this by .

Inverse of T

If is an isomorphism, then (the inverse) is also an isomorphism.

Dimension and Isomorphism

Let be vector spaces on with a finite dimension. Then, the following statements are equivalent:

  1. and are isomorphic

For instance, if is a vector space on such that , then .