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Frobenius matrix norm

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Frobenius norm

Let be an -matrix, and let be the norm in the underlying field (usually or with the standard norm (absolute value)). The Frobenius norm of is defined as

Note that this norm differs from the operator norm of (for instance because ; cf. Norm). If and are unitary matrices of appropriate size,

References

[a1] B. Noble, J.W. Daniels, "Applied linear algebra" , Prentice-Hall (1969) pp. 328ff (Edition: Second)
How to Cite This Entry:
Frobenius matrix norm. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Frobenius_matrix_norm&oldid=41548
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article