• RAVI S KULKARNI

      Articles written in Proceedings – Mathematical Sciences

    • Space of invariant bilinear forms

      RAVI S KULKARNI JAGMOHAN TANTI

      More Details Abstract Fulltext PDF

      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 $\mathbb{F} \neq 2$, 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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