Inverses of symmetric, diagonally dominant positive matrices and applications
نویسندگان
چکیده
We prove tight bounds for the ∞-norm of the inverse of a symmetric, diagonally dominant positive matrix J ; in particular, we show that ‖J‖∞ is uniquely maximized among all such J . 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 random graph distributions.
منابع مشابه
Tight bounds on the infinity norm of inverses of symmetric diagonally dominant positive matrices
We prove tight bounds for the ∞-norm of the inverse of symmetric diagonally dominant positive matrices. Applications include numerical stability for linear systems, bounds on inverses of differentiable functions, and the consistency of maximum entropy graph distributions from single samples.
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