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Journal of Applied Mathematics
Volume 2016, Article ID 4590817, 3 pages
http://dx.doi.org/10.1155/2016/4590817
Research Article

A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices

Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, Netherlands

Received 25 July 2016; Accepted 3 October 2016

Academic Editor: Frédéric Guichard

Copyright © 2016 Hal Caswell and Silke F. van Daalen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes.