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Matrix seminorms and related inequalities

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Abstract

One investigates estimates of the type ∥ABx∥⩽f(B)∥Ax∥, where A, B are matrices and x is a vector belonging to a certain subspace. One investigates the properties of the matrix seminorm f(B), in particular, its relation to the spectrum of the matrix B. For the case of a stochastic matrix B (which can be easily generalized to the case of a nonnegative matrix B) one derives estimates for f(B) which are convenient for practical computations (also on an electronic computer). One gives a numerical example illustrating the application of the results.

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Authors
  1. V. V. Kolpakov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 70, pp. 270–285, 1977.

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Kolpakov, V.V. Matrix seminorms and related inequalities. J Math Sci 23, 2094–2106 (1983). https://doi.org/10.1007/BF01093289

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  • DOI: https://doi.org/10.1007/BF01093289

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