Power inequalities and spectral dominance of generalized matrix norms |
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| Authors: | Charles R Johnson |
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| Institution: | Institute for Physical Science and Technology University of Maryland College Park, Maryland 20742 USA;Center for Applied Mathematics National Bureau of Standards Washington, D.C. 20234 USA |
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| Abstract: | A generalized matrix norm G dominates the spectral radius for all A?Mn(C) (i) if for some positive integer k the rule G(Ak) ? G(A)k holds for all A?Mn(C) and (ii) if and only if for each A?Mn(C) there exists a constant γA such that G(Ak) ? γAG(A)kfor all positive integers k. Other results and examples are also given concerning spectrally dominant generalized matrix norms. |
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