ما معنى Condition number, backward error, backward stability؟

The condition number of a problem bounds the relative change of its answer per relative change of its data; for solving $Ax = b$ it is $\kappa(A) = \lVert A\rVert\lVert A^{-1}\rVert$, the ratio of extreme singular values in the 2-norm. The backward error of a computed answer is the smallest perturbation of the data for which it is exact. An algorithm has backward stability if its backward error is always of the order of the unit roundoff.