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

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 2003Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Automatic Control, volume 48, pages 518-519 (issn: 0018-9286, eissn: 1558-2523,

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Authors: Seddik M. Djouadi;

doi: 10.1109/tac.2003.809159

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

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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.

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