matrix norm

A is a norm on the set$M_{m\times n}(R)$ of $m\times n$ matrices over a ring $R$, and isusually denoted by $||\cdot ||$.

The Frobenius matrix norm $||\cdot |{|}_F$ and the matrix $p$-norm (http://planetmath.org/MatrixPNorm) $||\cdot |{|}_p$are the most frequently used matrix norms.

A vector norm is a matrix norm for which the ring $R$ is a field.