>**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](https://en.wikipedia.org/wiki/Vibration) membranes exhibit an analogous property with respect to the unexcited state as the zero-level.

**Further edit:**  
[Laplacian Matrices](https://en.wikipedia.org/wiki/Laplacian_matrix) are integer valued examples of diagonally dominant matrices with vanishing row- and column sums.