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.
Hal Caswell. Silke F. van Daalen. "A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices." J. Appl. Math. 2016 1 - 3, 2016. https://doi.org/10.1155/2016/4590817