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Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
5
votes
Characterising semi-definite positiveness on vectors with non-negative entries
Your cone $C$ is the cone of copositive matrices. The dual of C is the cone of compeltely positive matrices. See e.g.
http://mathworld.wolfram.com/CopositiveMatrix.html
1
vote
Solving a System of Quadratic Equations
Groebner basis methods have already been mentioned as an approach to exactly solving this kind of system of equations. They aren't a way to find the best least squares solution in a case where there …