Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: non linear system, 6 unknowns, 6 equations (quadratic)
Replies: 5   Last Post: Jun 17, 2012 12:43 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Robert H. Lewis

Posts: 284
Registered: 12/8/04
Re: non linear system, 6 unknowns, 6 equations (quadratic)
Posted: Jun 17, 2012 12:43 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

> Hi,
>
> x1, x2, x3 are fixed vectors of R^3
> a=(a1,a2,a3) and t=(t1,t2,t3) are two unknown vectors
> of R^3. I is the 3,3 identity matrix
>
> Solve this system (the matrices in parenthesis are
> symmetric: only 6 eqns.):
> a1(x1*x1'-x1*t'-t*x1')+a2(x2*x2'-x2*t'-t*x2')+a3(x3*x3
> '-x3*t'-t*x3')=I
>
> Before trying to solve that numerically,
> any analytical result would be great
> (e.g., is there at least one solution ?).
>
> Thank you!
>
> Michel.


OK, reading some of the other posts I think I know what you mean. Evidently x_i are column vectors and you are using ' to mean transpose (looks weird to me).

Writing x1 as [ x11, x12, x13 ]', I got the 6 equations to be those printed below.

This system is solvable symbolically with resultants. For example, the resultant for a1 factors into polynomials of 6, 1, 12, and 5566 terms. If you are interested, let me know.

Robert H. Lewis
Fordham University





equations, set each to 0:
-2*x31*a3*t1 - 2*x21*a2*t1 - 2*x11*a1*t1 + x31^2*a3 + x21^2*a2 + x11^2*a1 - 1 ,
- x31*a3*t2 - x21*a2*t2 - x11*a1*t2 - x32*a3*t1 - x22*a2*t1 - x12*a1*t1 + x31*x32*a3 + x21*x22*a2 + x11*x12*a1 ,
- x31*a3*t3 - x21*a2*t3 - x11*a1*t3 - x33*a3*t1 - x23*a2*t1 - x13*a1*t1 + x31*x33*a3 + x21*x23*a2 + x11*x13*a1 ,
-2*x32*a3*t2 - 2*x22*a2*t2 - 2*x12*a1*t2 + x32^2*a3 + x22^2*a2 + x12^2*a1 - 1 ,
- x32*a3*t3 - x22*a2*t3 - x12*a1*t3 - x33*a3*t2 - x23*a2*t2 - x13*a1*t2 + x32*x33*a3 + x22*x23*a2 + x12*x13*a1 ,
-2*x33*a3*t3 - 2*x23*a2*t3 - 2*x13*a1*t3 + x33^2*a3 + x23^2*a2 + x13^2*a1 - 1



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.