Hi, I have a set of vectors that I would like to solve for in a nonlinear system of equations.(adsbygoogle = window.adsbygoogle || []).push({});

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}]=I

which 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}=0

So I dont know how to proceed. I would appreciate if anybody could point me in a direction, or to a matlab/scipy routine.

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# Solve Nonlinear System of Equations

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