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Bounded Groups and Norm-Hermitian Matrices
Emeric DeutschHans Schneider
出版Mathematics Research Center, University of Wisconsin, 1973
URLhttp://books.google.com.hk/books?id=17o2HQAACAAJ&hl=&source=gbs_api
註釋MATHEMATICS RESEARCH CENTERBounded Groups and Norm-Hermitian Matrices. Technical summary rept., Deutsch, Emeric ;Schneider, Hans ;MRC-TSR-1349DA-31-124-ARO(D)-462, NSF-GP-37978*Groups(Mathematics), *Matrices(Mathematics), TheoremsHermitian matricesAn elementary proof is given that a bounded multiplicative group of n x n complex (real) nonsingular matrices is similar to a unitary (orthogonal) group. Given a norm on complex n-space, it follows that there exists a nonsingular n x n matrix L (the Loewner-John matrix for the norm) such that LH(L sup ( -1)) is Hermitian for every norm-Hermitian H. Numerous applications of this result are given. (Author).