Matrix estimation problem

Imagine the following problem: we have a set of n matrix equations in the form of :

[b1] = [A] * [b0]

[b2] = [A] * [b1]

etc.

vertical vectors [b0], [b1], ... are GIVEN. We try to estimate matrix A. As there are many equations (more than cells in matrix A) the system has no solutions.

Is there any method that would allow to concisely write target function to estimate A by, for instance, minimizing sum of squares or applying other optimization technique?

([b1] - [A] * [b0])^2 + ([b2] - [A] * [b1])^2 + ... -> minimize

I have to input explicitly and symbolically the derivative of target function to the software.

Kind regards and thanks for help

J

Matrix estimation problem

Yes I did, but I couldn't get to the desired closed matrix formula. I believe that it is possible to explore the conditions and eventually use singular value decomposition, but at this moment I wasn't able to do it.

Thanks,