I'm not sure that I've understand what I'm doing when I'm trying to diagnolize the matrice.Maybe one of the reason of this is, I can't think it geometrically or I can't understand the purpose of this. So here it's my question : What if I've found different eigenvectors from others ? Is the result acceptable or matrice has one diagonal form? (I mean there's only one way to write diagonal of matrice). The definition of diagonal matrix says:
a diagonal matrix is a matrix (usually a square matrix) in which the entries outside the main diagonal (↘) are all zero. The diagonal entries themselves may or may not be zero.
İf my answer provides this definiton,does it mean that it's true?
(please edit my question for any language mistakes).