Weyl’s inequality


Let A and E be two n×n Hermitian matricesMathworldPlanetmath, with E positive semidefinitePlanetmathPlanetmath.

Let λi(A), λi(A+E), 1in be the eigenvaluesMathworldPlanetmathPlanetmathPlanetmathPlanetmath of A and A+E respectively, ordered in such a way that

|λ1||λ2||λn|.

Then

λi(A)λi(A+E).
Title Weyl’s inequality
Canonical name WeylsInequality
Date of creation 2013-03-22 15:33:37
Last modified on 2013-03-22 15:33:37
Owner Andrea Ambrosio (7332)
Last modified by Andrea Ambrosio (7332)
Numerical id 10
Author Andrea Ambrosio (7332)
Entry type Theorem
Classification msc 15A42