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
Canonical name	MatrixNorm
Date of creation	2013-03-22 11:43:20
Last modified on	2013-03-22 11:43:20
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	17
Author	mathcam (2727)
Entry type	Definition
Classification	msc 65F35
Classification	msc 43-02
Classification	msc 00A69
Related topic	VectorNorm
Related topic	FrobeniusMatrixNorm
Related topic	MatrixPnorm