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This note shows that we can recover any complex vector x0 ∈ Cn exactly from on the order of n quadratic equations of the form |hai, x0i|2 = bi, i = 1, . . . , m, by using a semidefinite program known ...
Abstract: We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by $2s$ for orientable equation and by $12s^4$ for no...
Abstract: We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutio...
We prove a bound for the geodesic diameter of a subset of the unit ball in Rn described by a fixed number of quadratic equations and inequalities,which is polynomial in n, whereas the known bound for ...

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