I’ve avoided proofs unless absolutely necessary, but the relation between the same eigenvector expressed in two different bases, is important.

Given that A_{S} is the linear transformation matrix in standard basis S, and A_{B} is its counterpart in basis B, we can write the relation between them as:

where C is the similarity transformation. We’ve seen this relation already; check here if you’ve forgotten about it.

Continue reading Matrix Theory: An essential proof for eigenvector computations