Space of invariant bilinear forms |
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Authors: | Ravi S Kulkarni Jagmohan Tanti |
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Institution: | 1.Bhaskaracharya Pratisthana,Pune,India;2.Central University of Jharkhand, CTI Campus,Ranchi,India |
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Abstract: | 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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