How can I guarantee the existence of a solution to this quadratic system of equations?












2












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I have $n$ real quadratic equations and $n$ real variables, $x_i$, of the following form:



$$sum_{ineq j} a_{ijk}x_ix_j+sum_ib_{ik}x_i+c_k=0 forall k$$



for $i,j,kin{1,dots n}$; all coefficients are real and I am interested in the existence of a real solution. Is there a condition on the coefficients to guaranty this?






algebraic-geometry systems-of-equations quadratic-forms







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    2












    $begingroup$


    I have $n$ real quadratic equations and $n$ real variables, $x_i$, of the following form:



    $$sum_{ineq j} a_{ijk}x_ix_j+sum_ib_{ik}x_i+c_k=0 forall k$$



    for $i,j,kin{1,dots n}$; all coefficients are real and I am interested in the existence of a real solution. Is there a condition on the coefficients to guaranty this?






    algebraic-geometry systems-of-equations quadratic-forms







    share|cite|improve this question











    $endgroup$















      2












      2








      2


      1



      $begingroup$


      I have $n$ real quadratic equations and $n$ real variables, $x_i$, of the following form:



      $$sum_{ineq j} a_{ijk}x_ix_j+sum_ib_{ik}x_i+c_k=0 forall k$$



      for $i,j,kin{1,dots n}$; all coefficients are real and I am interested in the existence of a real solution. Is there a condition on the coefficients to guaranty this?






      algebraic-geometry systems-of-equations quadratic-forms







      share|cite|improve this question











      $endgroup$




      I have $n$ real quadratic equations and $n$ real variables, $x_i$, of the following form:



      $$sum_{ineq j} a_{ijk}x_ix_j+sum_ib_{ik}x_i+c_k=0 forall k$$



      for $i,j,kin{1,dots n}$; all coefficients are real and I am interested in the existence of a real solution. Is there a condition on the coefficients to guaranty this?






      algebraic-geometry systems-of-equations quadratic-forms




      algebraic-geometry systems-of-equations quadratic-forms






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 3 at 16:08









      Ethan Bolker

      44k552117




      44k552117










      asked Jan 3 at 16:03









      Gabriel MartínezGabriel Martínez

      1027




      1027






















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