Matrix norm

Summary

A matrix norm is a norm on a space of matrices, often required to be submultiplicative: $\norm{AB} \le \norm{A} \norm{B}$. It measures the size of a matrix and so the size of errors and perturbations in matrix computations. The main examples are the operator norms induced by vector norms and the Frobenius norm. Every submultiplicative matrix norm bounds the spectral radius from above.