Null direction of a linear map ($v\ne 0,T(v)=0$)

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 $\mathrm{span}\{v\}$ 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.