## non-symmetric weak diagonal-dominant matrix, no decoupling: (a) is positive semi-definite? (b) has dim(ker)=1?

We are considering a matrix A=(aij)i,j=1,…,d∈Rd×d with the following property: aii=−∑j≠iaij, i.e., the matrix is not only weak diagonal-dominant, but its rows also sum up to 0. Note that the matrix is not necessarily symmetric (otherwise positive semi-definiteness would follow immediately from the weak diagonal-dominance). Furthermore, the matrix has the property that there are no … Read more