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Question:

is there a special name for matrices whose rows and columns sum to zero?

I actually need information about those matrices and thus a keyword for online search.

Edit: as there apparently is no name for those kind of matrices, I would like to suggest ,"Vibration Matrices" for discussion, because vibrating membranes exhibit an analogous property with respect to the unexcited state as the zero-level.

Further edit:
Laplacian Matrices are integer valued examples of diagonally dominant matrices with vanishing row- and column sums.

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Manfred Weis
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    This question looks relevant: https://mathoverflow.net/questions/293024/properties-of-zero-line-sum-matrices – Spencer Dembner Jul 25 '19 at 14:28
  • @Spencer, maybe you noticed that that question was posted by the user who has posted this one. – Gerry Myerson Jul 25 '19 at 23:12
  • Oh, I did not. Thanks for the heads up – Spencer Dembner Jul 25 '19 at 23:15
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    That was not on intent, I had forgotten about my earlier question, but still I would appreciate a keyword for those kind of matrices or, if there isn't one in use, suggestions for such a name. – Manfred Weis Jul 26 '19 at 03:37
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    Note that if $S$ is doubly-stochastic, then $S-I$ is your matrix. Maybe useful? – kjetil b halvorsen Jul 27 '19 at 13:34
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    @kjetilbhalvorsen true, but not all of 'my' matrices are of that structure because $|a_{ij}|\le 1$ for doubly stochastic matrices, whereas no such restriction exists for 'my' matrices. Of course every zero linesum matrix can be scaled to satisfy $\max(|a_{ij})|\in \lbrace 0,1\rbrace$ – Manfred Weis Jul 27 '19 at 15:29
  • I know $e$-matrices for constant raw sum. – Toni Mhax Jul 27 '19 at 15:44
  • @ToniMhax could you please provide further information about where I can find that name mentioned? – Manfred Weis Jul 27 '19 at 15:56
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    Yes i saw it here http://bkms.kms.or.kr/submission/Source/Download.php?FileDir=/201711/171187&FileName=B170964AOP.pdf – Toni Mhax Jul 27 '19 at 16:12
  • @ToniMhax in definition 1.4 of the article an $e-matrix$ is defined as a matrix for which $e$ (the all ones vector) is an eigenvector, so it seems to me that the term $e-matrix$ isn't used for constant row-sum matrices. – Manfred Weis Jul 27 '19 at 17:44

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