Find all possible solutions for a pseudo inverse

I met a problem when I calculate an equation.

R*P1 = P2

Here R is an 3*3 unknown matrix, P1 is a 3*1 column vector [3 2 1]', P2 is also a 3*1 column vector [10 22 34]'.

Now I try to calculate R. I used pinv in Matlab, it only give me one possible solution. As far as I know, there may be more than on solution for this equation. My question is if there is any matlab code or way to compute all possible solutions for R. Therefore I can select the best one.

Thank you

Ben

Answer 1

[Walter Roberson]

Effectively you have a linear system with 9 unknowns and 3 equations. There are going to be an infinite number of solutions with 6 unknowns. You could construct the vector space but you cannot compute all possible solutions in a finite time.

In order to "select the best one" you are going to need some criteria for what "best" is. Depending on what your criteria is, you might be able to compute the best solution instead of calculating all (infinity^6) possibilities and selecting the best of those afterwards.