proving that change of basis matrix is invertible.
Let say is the change of basis matrix from the base B to base C.
I need to prove that is invertible.
So that's what i did so far:
Now I tried to define the matrix (and to show its columns are linear independent), but this is where it got a little complicated for me:
since and B is basis for V, every vector can be represented as a linear combination of B's vectors:
and then, these equation can be written as:
Now, where is this change of basis matrix?
Is it the matrix with the entries?
Am I even writing it correctly?
Thanks in advanced!