# Linear operator

From AMS Glossary

## linear operator

- A mathematical operator that involves only a linear combination of terms or differentials in the dependent variable; examples are the del operator, the Laplacian operator, and the differential operator,
*L*wherethe coefficients*a*_{1}(*x*) · · ·*a*_{n}(*x*) may be functions of the independent variable*x*.

- A weighting function that is applied to past values of a time series in order to obtain estimates of future values, determined mathematically in such a way that the mean-square error of prediction is minimized.

This technique can be extended to more than one variable, so that many time series may be considered simultaneously.