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Comments on "Is the Frobenius Matrix Norm Induced?" [with reply]

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1 Author(s)
Djouadi, S.M. ; Syst. Eng. Dept., Univ. of Arkansas, Little Rock, AR, USA

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.

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Automatic Control, IEEE Transactions on  (Volume:48 ,  Issue: 3 )