# Weyl’s inequality

Let $A$ and $E$ be two $n\times n$ Hermitian matrices, with $E$ positive semidefinite.

Let $\lambda_{i}(A)$, $\lambda_{i}(A+E)$, $1\leq i\leq n$ be the eigenvalues of $A$ and $A+E$ respectively, ordered in such a way that

 $|\lambda_{1}|\leq|\lambda_{2}|\leq\cdots\leq|\lambda_{n}|.$

Then

 $\lambda_{i}(A)\leq\lambda_{i}(A+E).$
Title Weyl’s inequality WeylsInequality 2013-03-22 15:33:37 2013-03-22 15:33:37 Andrea Ambrosio (7332) Andrea Ambrosio (7332) 10 Andrea Ambrosio (7332) Theorem msc 15A42