Hi, my problem is simple enough to write down but (to me) seems quite difficult to solve.(adsbygoogle = window.adsbygoogle || []).push({});

My equation is as follows

A[x1 x2] = I.

Here I is some known matrix, and A is an operator which applies a shifting matrix and sums. That is A[x1 x2] = s1x1 + s2x2, where s1 and s2 are two shifting matrices (continuously it can be thought of as convolving with a delta function). x1 and x2 are two unknown matrices of the same dimension as I. Ultimately I wish to find a matrix form for A so that I can invert it and obtain x1 and x2

So as you can see [x1 x2] can be thought of as a "stack" of matrices, or a 3D matrix (or a tensor?). However I'm very unfamiliar with the mathematics of tensors so one idea I had was to convert x1 and x2 into columns (i.e., just shopping the matrix into slices and adding one ontop of the other). That way [x1 x2] would be a matrix, and I would have lost no information.

From here, however, I am very confused and not sure where to go.

If anyone has any ideas on what to do (or if this problem is impossible) it would be GREATLY appreciated, thanks!

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# Difficult linear algebra problem

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