Re: equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg3825] Re: equations*From*: peter at physto.se (Peter W)*Date*: Sat, 27 Apr 1996 00:58:38 -0400*Organization*: Stockholm University*Sender*: owner-wri-mathgroup at wolfram.com

In article <4l796a$1ov at ralph.vnet.net>, michael.probst at uibk.ac.at says... > >I have not seen my mail appearing in the newslist - >sorry if it's there twice. > >Hi, Experts ! >I have a mma - question concerning equation solving. >I understand how to use Solve and Eleminate for basic >problems but still my problem escapes me. >It's rather simple. >I have a rotation matrix rm: >MatrixForm[rm] >-0.772889 -0.568925 -0.28101 > 0.633718 -0.71461 -0.296198 >-0.0322979 -0.407009 0.912853 > >which I know must be equal to the rotation matrix qrm: > >MatrixForm[qrm] > 2 2 2 2 >q0 + q1 - q2 - q3 ........ > I used Solve on the four first eqs's and i got four complex sol's, I guess that if I use some combination of four other eq's I get other solutions in q but if the equations are consistent at least one solution should be common. I did: eqns={ q0^2 + q1^2- q2^2- q3^2==-0.772889 , 2 (q1 q2 - q0 q3)==-0.568925 , 2 (q0 q2 + q1 q3)==-0.28101, q1 q2 + q0 q3==0.633718} and: Solve[eqns,{q0,q1,q2,q3}] and I got: {{q0 -> -0.40173 - 0.0541109 I, q1 -> 0.0938041 - 0.231738 I, q2 -> 0.262086 + 0.647469 I, q3 -> -1.12242 + 0.151184 I}, {q0 -> -0.40173 + 0.0541109 I, q1 -> 0.0938041 + 0.231738 I, q2 -> 0.262086 - 0.647469 I, q3 -> -1.12242 - 0.151184 I}, {q0 -> -0.151184 - 1.12242 I, ....... By the way, there are methods for solving overdetermined equation systems (the solution will be the best fit to the equations in leastsquares sense) I have not done this in mma but with Matlab it is simple. I hope this helps /Peter Weijnitz ==== [MESSAGE SEPARATOR] ====