Matrix norm

In mathematics, the term matrix norm can have two meanings:

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• A vector norm on matrices, i.e, a norm on the vector space of all real or complex m-by-n matrices.
• A sub-multiplicative vector norm is any vector norm on square matrices compatible with matrix multiplication in the sense that

::|AB|le|A| |B|

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:The set of all n-by-n matrices, together with such a sub-multiplicative norm, is a Banach algebra.

Related Topics:
Set - Banach algebra

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In the rest of the article, we will follow the tradition in matrix theory. We use term "vector norm" for the first definition and "matrix norm" for the second definition.

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Matrix norm: Equivalence of norms ►