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## Main Question or Discussion Point

I have a matrix of the form X = [A B], where A and B are matrices of equal dimensions (M x N). I am looking for an elegant transformation to obtain Y = [A; B]. That is, the blocks are now stacked vertically.

Normally, I'd look for a solution of the form Y = VXW, where V is (2M x M) and W is (N x N/2). However, I feel that one may not exist in this case. For example, in the simplest case where A and B are scalars, then XW is scalar and so, in general, no V will exist which can give Y as required.

In that straightforward example, of course, we just use the transpose: Y = X

Any help would be greatly appreciated!

Normally, I'd look for a solution of the form Y = VXW, where V is (2M x M) and W is (N x N/2). However, I feel that one may not exist in this case. For example, in the simplest case where A and B are scalars, then XW is scalar and so, in general, no V will exist which can give Y as required.

In that straightforward example, of course, we just use the transpose: Y = X

^{T}. However, I cannot see how to generalise this for when A and B are matrices. (Or, actually, I'm hoping eventually to find a solution for stacking many matrices [A,B,C,...]).Any help would be greatly appreciated!