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.(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Linear Transformation to Block-wise Stack Matrix

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