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Recognition of Matrices Which are Sign-regular of a Given Order and a Generalization of Oscillatory Matrices

Recognition of Matrices Which are Sign-regular of a Given Order and a Generalization of Oscillatory Matrices

Type of Publication: Working Paper/Technical Report
Publication status: Accepted
URI (citable link): http://nbn-resolving.de/urn:nbn:de:bsz:352-2-11hoknygmukvc9
Author: AlSeidi, Rola; Garloff, Jürgen
Year of publication: 2020
Series: Konstanzer Schriften in Mathematik ; 392
Summary:
In this paper, rectangular matrices whose minors of a given order have the same strict sign are considered and sufficient conditions for their recognition are presented. The results are extended to matrices whose minors of a given order have the same sign or are allowed to vanish. A matrix is called oscillatory if all its minors are nonnegative and there exists a positive integer k such that Ak has all its minors positive. As a generalization, a new type of matrices, called oscillatory of a specific order, is introduced and some of their properties are investigated.
MSC Classification: 15B48, 15A15
Subject (DDC): 510 Mathematics
Keywords: Strict sign-regularity, sign-regularity, oscillatory matrix, compound matrix, primitive matrix, exponent of primitivity, oscillatory exponent of order k
Comment on publication: Wird erscheinen in: Operator and Matrices ; 2020. - Element, Zagreb
Link to License: In Copyright

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ALSEIDI, Rola, Jürgen GARLOFF, 2020. Recognition of Matrices Which are Sign-regular of a Given Order and a Generalization of Oscillatory Matrices

@techreport{AlSeidi2020Recog-50325, series={Konstanzer Schriften in Mathematik}, title={Recognition of Matrices Which are Sign-regular of a Given Order and a Generalization of Oscillatory Matrices}, year={2020}, number={392}, author={AlSeidi, Rola and Garloff, Jürgen}, note={Wird erscheinen in: Operator and Matrices ; 2020. - Element, Zagreb} }

2020 Garloff, Jürgen AlSeidi, Rola eng 2020-07-21T06:07:27Z AlSeidi, Rola 2020-07-21T06:07:27Z In this paper, rectangular matrices whose minors of a given order have the same strict sign are considered and sufficient conditions for their recognition are presented. The results are extended to matrices whose minors of a given order have the same sign or are allowed to vanish. A matrix is called oscillatory if all its minors are nonnegative and there exists a positive integer k such that A<sup>k</sup> has all its minors positive. As a generalization, a new type of matrices, called oscillatory of a specific order, is introduced and some of their properties are investigated. terms-of-use Garloff, Jürgen Recognition of Matrices Which are Sign-regular of a Given Order and a Generalization of Oscillatory Matrices

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