  We prove tight bounds for the $\infty$-norm of the inverse of symmetric,
diagonally dominant positive matrices. We also prove a new lower-bound form of
Hadamard's inequality for the determinant of diagonally dominant positive
matrices and an improved upper bound for diagonally balanced positive matrices.
Applications of our results include numerical stability for linear systems,
bounds on inverses of differentiable functions, and consistency of the maximum
likelihood equations for maximum entropy graph distributions.
