My question is very simple. How can we solve a vector equation involving the L2 norm, for example.
$$a + 2\frac{x}{\Vert x \Vert _2}=0$$
Even if a write it this way:
$$a + 2\frac{x}{\sqrt{\sum_i x_i^2}}=0$$
where $a$ is a real value vector with same dimension as $x$
I am not able to continue.
Thanks.
$a$ has to be vector of length $2$, and hence we need $-\frac{a}2$ to be a unit vector.
We have $$\frac{x}{\|x\|_2}=-\frac{a}2$$
Any positive multiple of $-a$ is then a possible solution.