Numerical radius and zero pattern of matrices
نویسندگان
چکیده
منابع مشابه
Numerical radius and zero pattern of matrices
Let A be an n n complex matrix and r be the maximum size of its principal submatrices with no o¤-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting kAk be the Frobenius norm of A; we show that jhAx;xij (1 1=2r 1=2n) kAk : This inequality is tight within an additive term O n 2 : If the matrix A is Hermitian, then jhAx;xij (1 1=r) kAk : This inequality...
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Let F (A) be the numerical range or the numerical radius of a square matrix A. Denote by A◦B the Schur product of two matrices A and B. Characterizations are given for mappings on square matrices satisfying F (A ◦ B) = F (φ(A) ◦ φ(B)) for all matrices A and B. Analogous results are obtained for mappings on Hermitian matrices. 2000 Mathematics Subject Classification. 15A04, 15A18, 15A60
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.04.042