= Null direction of a linear map
{title2=$v\ne0,\quad T(v)=0$}
= Null directions of a linear map
{synonym}
A <null direction of a linear map> $T$ is represented by a nonzero <vector> $v$ in its <kernel>. Every <scalar multiple> $tv$ is an undetectable displacement: $T(x+tv)=T(x)$. The <vector subspace> $\operatorname{span}\{v\}$ describes the direction independently of the chosen nonzero representative. More generally, a <basis> of the <kernel> supplies all independent <null directions of a linear map>; their number is the <nullity>. The <zero vector> belongs to the <kernel> but supplies no direction.
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