Frobenius matrix norm
From Encyclopedia of Mathematics
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=11565
Frobenius matrix norm. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Frobenius_matrix_norm&oldid=11565
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article