I am designing an algorithm, in which an intermediate step is to create a $n\times n$ invertible non-negative matrix. The idea that I thought was to choose a random generator $P$ to generate $n^2$ points and then make a matrix $A$ by reshaping. Then do a $A^TA$ to make it non-negative and then $B=I+A^TA$ to make it invertible. But the problem is that since B is a symmetric matrix that will be a drawback for my algorithm which I don't need. Can somebody suggest any readings or methods that construct the non-negative matrix? Edit: B should be a matrix whose entries are uncorrelated. The matrix $B$ should be sparse
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$\begingroup$ Make one of these en.wikipedia.org/wiki/Diagonally_dominant_matrix $\endgroup$– Michal AdamaszekMay 8, 2018 at 12:34
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$\begingroup$ The construction you propose yields - assuming a $\mathbb R$eal context - a symmetric positive matrix $M\geqslant 1_{n\times n}$, hence $M$ is invertible. But it does not become clear why such an $M$ is not suited for your purpose; your second-to-last sentence is hard to grasp and (at least) grammatically incorrect. It would be helpful to make your question more concise, especially the properties you want $M$ to satisfy. Have you seen Algo for PSD matrices (which is on top of the "Related Posts" column?) $\endgroup$– HannoMay 8, 2018 at 12:59
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$\begingroup$ actually i need a random matrix that is the data entries should be uncorrelated. I need it in an encryption algorithm $\endgroup$– UpstartMay 8, 2018 at 14:10
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$\begingroup$ Your description is still not clear, it remains ambiguous: $A^TA$ is always a positive-semidefinite matrix, for any $A$. Whereas a non-negative matrix is one with all entries $\geq0$. Note that multiplication of $A^T$ with $A$ may produce negative entries (quickly to find in $2\times2$-matrices), hence $A^TA$ is not a non-negative matrix in general. So what are you aiming for? $\endgroup$– HannoMay 9, 2018 at 22:15
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