Geodesic
Matrix seminorms and related inequalities
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 70 (1977), pp. 270-285

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One investigates estimates of the type $\|ABx\|\leqslant f(B)\|Ax\|$, 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. 
@article{ZNSL_1977_70_a18,
     author = {V. V. Kolpakov},
     title = {Matrix seminorms and related inequalities},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {270--285},
     publisher = {mathdoc},
     volume = {70},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_70_a18/}
}
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PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1977_70_a18/
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ID  - ZNSL_1977_70_a18
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%A V. V. Kolpakov
%T Matrix seminorms and related inequalities
%J Zapiski Nauchnykh Seminarov POMI
%D 1977
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%F ZNSL_1977_70_a18
V. V. Kolpakov. Matrix seminorms and related inequalities. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 70 (1977), pp. 270-285. http://geodesic.mathdoc.fr/item/ZNSL_1977_70_a18/