I have these questions and cannot find a proof in the textbook: when one finds eigenvectors of a matrix they form its eigenspace, i.e. they are lin indep, how is it proved? And also a matrix is deficient, when one does not get "enough" eigenvectors to span R^n, so maybe I am wrong, but it seems that the technique of finding eigenvectors eliminates lin dependent eigenvectors if there were such. How so? Thanks as usual!