Level numbers of a bounded linear operator between normed linear spaces and singular value decomposition revisited

Sain, D and Roy, S and Tanaka, R (2020) Level numbers of a bounded linear operator between normed linear spaces and singular value decomposition revisited. In: Linear and Multilinear Algebra .

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Abstract

We introduce the notion of level numbers of a bounded linear operator between normed linear spaces, as a generalization of the singular values of an operator between inner product spaces. We study the geometric and the analytic properties of the level numbers, in connection with Birkhoff–James orthogonality and norm optimization problems. We also illustrate the similarities and the differences between the level numbers and the singular values of an operator. As an application of the present study, we obtain a new and elementary approach to the singular value decomposition of matrices.

Item Type:	Journal Article
Publication:	Linear and Multilinear Algebra
Publisher:	Taylor and Francis Ltd.
Additional Information:	The copyright for this article belongs to Taylor and Francis Ltd.
Keywords:	adjoint operator; Birkhoff–James orthogonality; Level number; singular value decomposition
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	07 Feb 2023 09:36
Last Modified:	07 Feb 2023 09:36
URI:	https://eprints.iisc.ac.in/id/eprint/80002

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