Definition of matrix norms

In my previous post, I introduced various definitions of matrix norms in \(\mathbb{R}^{n \times n}\) based on the corresponding vector norms in \(\mathbb{R}^n\). Meanwhile, the equivalence of different vector norms and their induced metrics and topologies in \(\mathbb{R}^n\) is also inherited into \(\mathbb{R}^{n \times n}\). In this article, we’ll show why the above defined matrix norms are valid., I introduced various defini