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matrix norm (Definition)

A matrix norm 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 $ \vert\vert\cdot\vert\vert$.

The Frobenius matrix norm $ \vert\vert\cdot\vert\vert _F$ and the matrix $ p$-norm $ \vert\vert\cdot\vert\vert _p$ are the most frequently used matrix norms.

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



"matrix norm" is owned by mathcam. [ full author list (3) | owner history (2) ]
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See Also: vector norm, Frobenius matrix norm, matrix p-norm

Keywords:  frobenius
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Cross-references: field, vector norm, Frobenius matrix norm, ring, matrices, norm
There are 9 references to this entry.

This is version 7 of matrix norm, born on 2001-10-06, modified 2006-07-24.
Object id is 106, canonical name is MatrixNorm.
Accessed 22046 times total.

Classification:
AMS MSC: 65F35 (Numerical analysis :: Numerical linear algebra :: Matrix norms, conditioning, scaling)
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