DocumentCode
1159117
Title
Comments on "Is the Frobenius Matrix Norm Induced?" [with reply]
Author
Djouadi, Seddik M.
Author_Institution
Syst. Eng. Dept., Univ. of Arkansas, Little Rock, AR, USA
Volume
48
Issue
3
fYear
2003
fDate
3/1/2003 12:00:00 AM
Firstpage
518
Lastpage
519
Abstract
In "Is the Frobenius matrix norm induced?", the authors ask whether the Frobenius and the H/sup 2/ norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the H/sup 2/ norm may not be induced. In this paper, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the H/sup 2/ norm is in fact induced on a particular matrix-valued L/sup /spl infin// space. A reply is provided to the comments.
Keywords
matrix algebra; Frobenius matrix norm; H/sup 2/ norms; matrix-valued L/sup /spl infin// space; Control systems; Systems engineering and theory;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2003.809159
Filename
1184912
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