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Is the Frobenius matrix norm induced?

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2 Author(s)
Chellaboina, V.-S. ; Sch. of Aerosp. Eng., Georgia Inst. of Technol., Atlanta, GA, USA ; Haddad, M.M.

In this paper we answer the question of whether (or not) there exist normed input-output vector spaces that induce the Frobenius matrix norm. Specifically, using the notion of dual norms we show that, up to a scalar multiple, the maximum singular value is the only unitarily invariant induced norm. As a special case of this result, it follows that the Frobenius matrix norm is not induced

Published in:

Automatic Control, IEEE Transactions on  (Volume:40 ,  Issue: 12 )