Mixing
How can I guarantee the existence of a solution to this quadratic system of equations?
$begingroup$
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
edited Jan 3 at 16:08
Ethan Bolker
42.1k548111
asked Jan 3 at 16:03
Gabriel MartínezGabriel Martínez
1027
$endgroup$
add a comment |
$begingroup$
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
edited Jan 3 at 16:08
Ethan Bolker
42.1k548111
asked Jan 3 at 16:03
Gabriel MartínezGabriel Martínez
1027
$endgroup$
add a comment |
$begingroup$
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
edited Jan 3 at 16:08
Ethan Bolker
42.1k548111
asked Jan 3 at 16:03
Gabriel MartínezGabriel Martínez
1027
$endgroup$
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
edited Jan 3 at 16:08
Ethan Bolker
42.1k548111
asked Jan 3 at 16:03
Gabriel MartínezGabriel Martínez
1027
edited Jan 3 at 16:08
Ethan Bolker
42.1k548111
asked Jan 3 at 16:03
Gabriel MartínezGabriel Martínez
1027
edited Jan 3 at 16:08
Ethan Bolker
42.1k548111
edited Jan 3 at 16:08
Ethan Bolker
42.1k548111
edited Jan 3 at 16:08
Ethan Bolker
42.1k548111
42.1k548111
asked Jan 3 at 16:03
Gabriel MartínezGabriel Martínez
1027
asked Jan 3 at 16:03
Gabriel MartínezGabriel Martínez
1027
asked Jan 3 at 16:03
Gabriel MartínezGabriel Martínez
1027
1027
add a comment |
add a comment |
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