Name for a vector

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Given a matrix $B\in\Bbb R^{n\times n}$ what do we call vectors $v$ such that for $$v'Bv=0$$ holds?

Is there a name for these?

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Interpreting $B$ as a bilinear form, these are called null vectors. (The zero vector is usually excluded.) As Will Jagy mentions, the entire set is called the null cone for the form.