I need to find $v$ so that $v\times v'$ equals $A(n \times n)$

Question

Be $A_{n\times n}$ symmetric.

I need to find $v_{m\times n}$ so that $v^T \times v = A$ for an algorithm in Julia.

Can anyone help me (either w/ Julia or linear algebra)?

Answer 1

If your matrix rank is more that 1 this is impossible and for rank 1 we have $$v=\begin{bmatrix}v_1\\v_2\\.\\.\\.\\v_n\end{bmatrix}\to v\times v^T=\begin{bmatrix}v_1.v&v_2.v&.&.&.&v_n.v\end{bmatrix}$$which is obviously of rank 1