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.
"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