Usually, a matrix equation means that $$ Ax = b $$ when A and b are given and x is the variable we want to know.
However, when x and b are given and we want to know the value of the matrix, is it acheivable?
To provide context, I'm studying quantum computing and I tried to figure out if a certain state vector can be derived from $ |00...0 \rangle $ with unitary transformations. So you can assume $ A $ is unitary and $ b $ is $ |00...0 \rangle $.
Now I'm almost brute-forcing to solve this kind of equation, so even though there is no general algorithm for it, just giving some tips and tricks would also be very helpful.