Left radical of a bilinear form
= Left radical of a bilinear form
{title2=$\operatorname{rad}_L B=\ker A^T$}
= Left radical
{synonym}
The <left radical> is $\{v\in V:B(v,w)=0\text{ for every }w\in V\}$. If $A$ is the <matrix of a bilinear form>, this condition is $v^TA=0$, so its <coordinate vectors> form $\ker A^T$. For $A=\begin{pmatrix}0&1\\0&0\end{pmatrix}$, the <bilinear form> $B(v,w)=v_1w_2$ has <left radical> $\operatorname{span}\{(0,1)\}$.