= Right radical of a bilinear form
{title2=$\operatorname{rad}_R B=\ker A$}
= Right radical
{synonym}
The <right radical> is $\{w\in V:B(v,w)=0\text{ for every }v\in V\}$. If $A$ is the <matrix of a bilinear form>, this condition is $Aw=0$. For $B(v,w)=v_1w_2$ from the <left radical> example, the <right radical> is $\operatorname{span}\{(1,0)\}$. The <left radical> and <right radical> differ here because the <bilinear form> is neither symmetric nor alternating. For a <symmetric bilinear form> or an <alternating bilinear form>, reversing a zero pairing preserves zero and the two <linear subspaces> coincide.
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