Abstract: In this paper, to symmetrical matrix (diagonalizable matrix), we have studied arbitrary perturbation and real arbitrary perturbation of it (with real eigenvalue arbitrary perturbation). It is started with to resolve from everybody known very well Schur decomposition, utilizing matrix that can be diagonalizable and identically equal through matrix equality out of shape, receiving perturbation bounds of diagonalizable matrix about F-norm and Q-norm.