Doubly stochastic matrix

From Glossary of Meteorology

doubly stochastic matrix

A (usually square) matrix for which the sum of each row and each column equals one.

An example is a transilient matrix used to describe vertically nonlocal turbulent mixing in the atmosphere, where the sum of each column must equal one to conserve a state such as heat or moisture, and the sum of each row must equal one to conserve air mass. The largest eigenvector of a doubly stochastic matrix is not larger than unity, which implies absolute numerical stability for any time step and any grid spacing when using the matrix to make forecasts of turbulent mixing.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact 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.