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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)?

Gabriel Milan
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    Certainly not every $n\times n$ matrix that is symmetric is of rank $1$. Or are you assuming $A$ is of rank $1$? – Pedro Mar 07 '18 at 19:42
  • Sorry, I wrote it wrong. Just fixed my question – Gabriel Milan Mar 07 '18 at 20:29
  • To write $A = BB^t$, I think you want to assume $A$ is positive semidefinite, right? – Pedro Mar 07 '18 at 20:32
  • For better undestanding, check this question: https://math.stackexchange.com/questions/2681367/building-matrix-so-that-the-inner-product-of-columns-results-in-an-element-of-an Sorry about all the mess – Gabriel Milan Mar 07 '18 at 21:26

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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

Mostafa Ayaz
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