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单词 HadamardsInequality
释义

Hadamard’s inequality


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

|det(A)|i=1n(j=1n|aij|2)12.

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

det(A)i=1naii,

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

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更新时间:2025/5/5 12:49:54