# An extension of inequalities by Ando

## TL;DR

This paper extends Ando's inequalities by exploring variations that compare differences of functions of matrices and their absolute differences using unitarily invariant norms.

## Contribution

It introduces new variations of Ando's inequalities, broadening their applicability in matrix analysis and operator theory.

## Key findings

- Derived new inequalities relating $f(B)-f(A)$ and $f(|B-A|)$
- Extended the scope of Ando's inequalities to broader classes of functions
- Provided bounds for unitarily invariant norms in matrix comparisons

## Abstract

We give variations on Ando's result comparing $f(B)-f(A)$ and $f(|B-A|)$ with respect to unitarily invariant norms on matrices.