Linear Time-Invariant System

A Linear Time-Invariant (LTI) System a Linear Transformation where shifting time in the input signal shifts the time everywhere in the output signal by the same amount.

Linear Transformation

$$\begin{array}{rl}T(x_1[n]+x_2[n])& =T(x_1[n])+T(x_2[n])\\ T(\lambda x_1[n])& =\lambda T(x_1[n])\end{array}$$

Time Invariance

$$T(x[n-n_0])=y[n-n_0]$$

See Shift-Invariance, which is the same as this.