Hadamard’s inequality

Let A=(aij) with 1i,jn be a square matrixMathworldPlanetmath with complex coefficients. Then the following inequalityMathworldPlanetmath holds:


Moreover, if A is Hermitian and positive semidefinitePlanetmathPlanetmath, the following inequality holds:


with equality if and only if A is a diagonal matrixMathworldPlanetmath.

Title Hadamard’s inequality
Canonical name HadamardsInequality
Date of creation 2013-03-22 14:32:21
Last modified on 2013-03-22 14:32:21
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 9
Author mathwizard (128)
Entry type Theorem
Classification msc 15A45