Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Just a quick terminology question.

The set of solutions to a linear system of equations with nonunique solutions is known as the "nullspace".

What is the equivalent terminology (if there is one) for the nonunique solutions to a nonlinear system of equations? (or its equivalent Groebner basis)

For example: $$ \begin{align} &x_{1} + x_{2}^{2} + 3x_{3}= 0\\ &x_{3} = 2 \end{align} $$

Is there a name this set of solutions? The solutions of the above system is: $$ \begin{align} &x_{1} = -6 -t^{2}\\ &x_{2} = t\\ &x_{3} = 2 \end{align} $$

share|improve this question
4  
Maybe the locus? If the linearised system always have the same nullity, then you may even talk about the solution manifold. –  Willie Wong Apr 26 '11 at 18:10
    
I'm with Willie; locus sounds about right. Geometrically your nonunique set of solutions would correspond to some curve/surface... –  J. M. Apr 26 '11 at 18:19
    
I'm torn here: I think both Willie's and lhf's answers have merit, and I'm not sure which one I should accept. Willie, if you would care to make your comment and answer, I'd be happy to upvote (and let others do the same). –  Gilead Apr 27 '11 at 1:06

1 Answer 1

Zero set is a usual term. But so is set of solutions. Zero set is applied to sets of functions. Set of solutions is applied to systems of equations.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.