Timeline for Is the following DNN matrix CP?
Current License: CC BY-SA 3.0
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| Jul 29, 2011 at 6:19 | comment | added | Gerhard Paseman | Pawan, I sometimes "enhance" answers (by adding what I think are relevant comments) for the benefit of the original poster and for future readers. I apologize for any slight (regarding what you may know or may not know) I may have caused. The problem reminds me of the search for 0-1 matrices with maximal determinant, and I thought that literature might be of use. When you are ready to share more, I invite you to do so. Gerhard "Ask Me About System Design" Paseman, 2011.07.28 | |
| Jul 29, 2011 at 4:46 | comment | added | Pawan Aurora | When I say that a matrix is doubly non-negative, it is implied that the matrix is a gram matrix and thus can be written in the form $G=MM^T$. What I am really concerned about is that such a factorization exists with non-negative $M$. This problem is still open for general matrices $G$, although for specific cases it is solved. I am hoping that the kind of matrices that I get fall into some specific category or can be derived from known results. | |
| Jul 29, 2011 at 3:32 | comment | added | Gerhard Paseman | In my reading of the literature on 0-1 matrices, $G$ is a Gram matrix where $G = MM^T$ and $M$ is some special matrix (for me a square 0-1 matrix, although the definition may be more general) . I suggest looking at Gram matrix literature if you are going to deal with matrices like the one in your question. Also, Will Orrick might be a good person to consult for more detail. Gerhard "Ask Me Not About Transpose" Paseman, 2011.07.28 | |
| Jul 29, 2011 at 3:25 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
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| Jul 29, 2011 at 2:54 | vote | accept | Pawan Aurora | ||
| Jul 29, 2011 at 2:53 | comment | added | Pawan Aurora | @Gerhard Paseman, I am trying to show that the matrices resulting out of an optimization problem are CP. Although not all matrices will have the same structure as the one I posted. Definitely this is not a homework problem. | |
| Jul 29, 2011 at 2:14 | comment | added | Robert Israel | Make that $W^T$ and you're correct. | |
| Jul 29, 2011 at 1:59 | comment | added | Gerhard Paseman | Also (assuming the answer helps), I would like in return to know the motivation for the problem. In particular, if I have helped to solve a homework problem, I want the grader to give me some of the credit. Gerhard "Maintain A Good Credit Score" Paseman, 2011.07.28 | |
| Jul 29, 2011 at 1:55 | comment | added | Gerhard Paseman | I did this by hand, and left out the zeroes for readability. I apologize conditionally for any errors in this answer. Gerhard "Ask Me About System Design" Paseman, 2011.07.28 | |
| Jul 29, 2011 at 1:50 | history | answered | Gerhard Paseman | CC BY-SA 3.0 |