Abstract:
In this paper, both well-known and new properties of the spectral abscissa and the logarithmic norm are described. In addition to well-known formulas for the norm of a matrix and for its logarithmic norm in cubic, octahedral, spherical norms, various estimates for these quantities in an arbitrary Hölder norm are proved.
Keywords:spectral radius and the norm of a matrix, spectral abscissa and the logarithmic norm of a matrix, Young's inequality, Hölder's inequality, Riesz theorem, Hölder norm.
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