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.