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












2














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














    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



























      2












      2








      2


      1





      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















      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 2 days ago









      Ethan Bolker

      41.7k547110




      41.7k547110










      asked 2 days ago









      Gabriel Martínez

      1027




      1027






















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