Topics: Algebra - Linear Transformation


Let be vector spaces on where , , .


  • be a basis of
  • be a basis of
  • be a basis of

…and let and be linear transformations.

Then, the associated matrix of (composition) is:

Inverse Transformations and Isomorphism


Let be an Isomorphism.

  • is linear; is also linear.
  • Let be a basis of
  • Let be a basis of

Then, the associated matrix to is:

…and the associated matrix to is its inverse matrix:

Furthermore, let’s remember that and that (identity transformations). With this, then we have that:

…where denotes the respective identity matrices.