# Linear operator

From Glossary of Meteorology

## 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.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact [email protected]. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.