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BY 4.0 license Open Access Published by De Gruyter Open Access January 8, 2019

Some matrix properties preserved by generalized matrix functions

  • Michele Benzi EMAIL logo and Ru Huang
From the journal Special Matrices


Generalized matrix functions were first introduced in [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163-171]. Recently, it has been recognized that these matrix functions arise in a number of applications, and various numerical methods have been proposed for their computation. The exploitation of structural properties, when present, can lead to more efficient and accurate algorithms. The main goal of this paper is to identify structural properties of matrices which are preserved by generalized matrix functions. In cases where a given property is not preserved in general, we provide conditions on the underlying scalar function under which the property of interest will be preserved by the corresponding generalized matrix function.

MSC 2010: 15A16


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Received: 2018-08-16
Accepted: 2018-11-17
Published Online: 2019-01-08

© by Michele Benzi, Ru Huang, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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