Solution
= Solution
The origin is feasible and has objective zero, while a <Euclidean norm> is nonnegative. Thus \b[the <minimum> is $0$], and the complete <argmin> is
$$
\boxed{\ker A\cap\{\mathbf x:\|\mathbf x\|\le1\}.}
$$
If $A$ is <injective>, this set contains only the origin. If it has a nontrivial <kernel>, every feasible <kernel> vector is also a minimizer. No <Lagrange multipliers> are needed.