Mortini, Raymond, Rupp, Rudolf and Sasane, Amol J. (2010) Matricial topological ranks for two algebras of bounded holomorphic functions. Linear and multilinear algebra, 58 (6). pp. 741-752. ISSN 0308-1087
Let N and D be two matrices over the algebra H ∞ of bounded analytic functions in the disk, or its real counterpart . Suppose that N and D have the same number n of columns. In a generalization of the notion of topological stable rank 2, it is shown that N and D can be approximated (in the operator norm) by two matrices Ñ and , so that the Aryabhatta–Bezout equation admits a solution. This has particular interesting consequences in systems theory. Moreover, in case that N is a square matrix, X can be chosen to be invertible in the case of the algebra H ∞, but not always in the case of .
|Additional Information:||© 2010 Taylor & Francis|
|Uncontrolled Keywords:||topological stable rank, Hardy algebra, control theory|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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