I was wondering there is an elegant solution for
$$\sum_i J_i \left(J_i^T x - 1 \right) = 0$$
where $x, J_i \in \mathbb{R}^n$ are vectors. Also all $J_i$ have the same norm.
I thought of having such approch
$$\sum_i J_i \left(||J_i|| \cdot ||x|| \cdot cos(\phi_i) - 1 \right) = 0 \\ ||J_i|| \cdot \sum_i J_i \left(||x|| \cdot cos(\phi_i) - 1 \right) = 0 $$
Has anyone thoughts on this? Thanks
I am aware that I can use an Cholesky-factorization if $\sum_i J_i \cdot J_i^T$ is positive-definite but I wanted to try something else.