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I have tried to use scipy.fsolve to solve the system, but without success. I believe the problem is that scipy expects the same number of inputs as outputs. I have a 12x1 input vector, but I can only generate 9 independent equations.

I would appreciate any help with this, for example how I could over-constrain the problem, or am I missing something?

The vectors {

*} are all (3x1). There are also a set of (3x1) vectors {*

**C,R**_{1},R_{2},R_{3}*} that are known.*

**S**_{1},S_{2},S_{3}The equations are as follows:

*(1)*

**C**^{T}R_{1}=S_{1}*(2)*

**C**^{T}R_{2}=S_{2}*(3)*

**C**^{T}R_{3}=S_{3}and finally

**[R**_{1}R_{2}R_{3}]^{T}[R_{1}R_{2}R_{3}]=Iwhich can be reduced to

*(4,5,6)*

**R**_{1}^{T}R_{1}=R_{2}^{T}R_{2}=R_{3}^{T}R_{3}=1*(7,8,9)*

**R**_{1}^{T}R_{2}=R_{2}^{T}R_{3}=R_{3}^{T}R_{1}=0*Would give me 12 equations, but they are exactly the same as Equations 7,8,9.*

**R**_{2}^{T}R_{1}=R_{3}^{T}R_{2}=R_{1}^{T}R_{3}=0So I dont know how to proceed. I would appreciate if anybody could point me in a direction, or to a matlab/scipy routine.