Topics: Algebra - Linear Transformation - Vector Space - Associated Matrix of a Linear Transformation

Let be a linear transformation.


Let and be ordered bases of , and and ordered bases of .

With the associated matrices of under these bases, we have that:

…where is the change of basis matrix from to , and the change of basis matrix that from to .


Let be a linear transformation, with ordered bases and . Then:

…where is the basis change matrix from to .