Quadratic maps in two variables on arbitrary fields. (English) Zbl 1488.15046
Summary: Let \(\mathbb{F}\) be a field of characteristic different from 2 and 3, and let \(V\) be a vector space of dimension 2 over \(\mathbb{F}\). The generic classification of homogeneous quadratic maps \(f : V\to V\) under the action of the linear group of \(V\), is given and efficient computational criteria to recognize equivalence are provided.
MSC:
15A72 | Vector and tensor algebra, theory of invariants |
11E88 | Quadratic spaces; Clifford algebras |
12E20 | Finite fields (field-theoretic aspects) |
12E30 | Field arithmetic |
13A50 | Actions of groups on commutative rings; invariant theory |
15A66 | Clifford algebras, spinors |