Abstract: In this paper, the authors give the characterization of both linear automorphisms and linear flows on Rⁿ with the limit shadowing property. That is, an automorphism defined by a matrix has the limit shadowing property if and only if this matrix is hyperbolic, and a linear flow induced by a matrix has the limit shadowing property if and only if all
eigenvalues of this matrix have nonzero real parts.

Key words: Limit shadowing property, Linear automorphism, Linear flow, Hyperbolicity