# Wielandt-Hoffman theorem

Let $A$ and $B$ be normal matrices (http://planetmath.org/NormalMatrix). Let their eigenvalues $a_{i}$ and $b_{i}$ be ordered such that $\sum_{i}|a_{i}-b_{i}|^{2}$ is minimized. Then we have the following inequality

 $\sum_{i}|a_{i}-b_{i}|^{2}\leq\|A-B\|_{F}^{2},$

where $\|\cdot\|_{F}$ is the Frobenius matrix norm.

Title Wielandt-Hoffman theorem WielandtHoffmanTheorem 2013-03-22 14:58:45 2013-03-22 14:58:45 Andrea Ambrosio (7332) Andrea Ambrosio (7332) 4 Andrea Ambrosio (7332) Theorem msc 15A42 msc 15A18 ShursInequality