Quadratic maps in two variables on arbitrary fields

Durán Díaz, R., Hernández Encinas, L. and Muñoz Masqué, J.

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carpathian_2021_37_1_91_100

Issue no: Vol 37/2021 no. 1 Tags: linear representation, linear group, symmetric bilinear composition law, Clifford algebra, homogeneous quadratic map, invariant function

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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 $f\colon V\to V$ under the action of the linear
group of $V$ , is given and efficient computational criteria to recognize equivalence are provided.