Space of invariant bilinear forms
Tóm tắt
Let
$${\mathbb {F}}$$
be a field, V a vector space of dimension n over
$${\mathbb {F}}$$
. Then the set of bilinear forms on V forms a vector space of dimension
$$n^2$$
over
$${\mathbb {F}}$$
. For char
$${\mathbb {F}}\ne 2$$
, if T is an invertible linear map from V onto V then the set of T-invariant bilinear forms, forms a subspace of this space of forms. In this paper, we compute the dimension of T-invariant bilinear forms over
$${\mathbb {F}}$$
. Also we investigate similar type of questions for the infinitesimally T-invariant bilinear forms (T-skew symmetric forms). Moreover, we discuss the existence of nondegenerate invariant (resp. infinitesimally invariant) bilinear forms.
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