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- W2009303079 abstract "Given n×n complex matrices A, C, the C-numerical radius of A is the nonnegative quantity rc(A)≡ma{|tr(CU∗AU)|:U unitary}. For C=diag(1,0,…,0) it reduces to the classical numerical radius r(A)= max{|x∗Ax|:x∗x=1}. We show that rc is a generalized matrix norm if and only if C is nonscalar and trC≠0. Next, we consider an arbitrary generalized matrix norm and characterize all constants v⩾0 for which vN is multiplicative. A technique to obtain such v is then applied to C-numerical radii with Hermitian C. In particular we find that vr is a matrix norm if and only if v⩾4." @default.
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- W2009303079 date "1979-04-01" @default.
- W2009303079 modified "2023-10-14" @default.
- W2009303079 title "Norm properties of C-numerical radii" @default.
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- W2009303079 doi "https://doi.org/10.1016/0024-3795(79)90152-6" @default.
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