# matrix norm

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

Title matrix norm MatrixNorm 2013-03-22 11:43:20 2013-03-22 11:43:20 mathcam (2727) mathcam (2727) 17 mathcam (2727) Definition msc 65F35 msc 43-02 msc 00A69 VectorNorm FrobeniusMatrixNorm MatrixPnorm