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Results tagged with quadratic-forms
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user 5963
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.
4
votes
how to determine a biquadratic form is positive-definite
In general one doesn't expect to have nice necessary and sufficient conditions for checking positivity of a biquadratic form. The sum-of-squares methods outlined in these course notes provide an effi …
- 8,501
10
votes
Accepted
Characterising semi-definite positiveness on vectors with non-negative entries
The cone $C$ is called the cone of copositive matrices and its dual $C^*$ is called the cone of completely positive matrices. Here are some references.
The paper most relevant to your question is pr …
- 8,501
4
votes
Accepted
Decide how many non-negative solutions a set of multivariate quadratic equations have
Not efficiently, at least not unless the problem has some additional structure which can be exploited. The set of mixed Nash equilibria of a two-player game can be written as the nonnegative solution …
- 8,501
2
votes
Solving a System of Quadratic Equations
What you have is an instance of a quadratically constrained quadratic program (QCQP). These problems are NP-hard in general (though it's possible your particular type of instance is not hard as fedja …
- 8,501