Publisher DOI: 10.13001/1081-3810.3910
Title: The determinant of a complex matrix and Gershgorin circles
Language: English
Authors: Bünger, Florian 
Rump, Siegfried M. 
Keywords: Gershgorin circle;Determinant;Minkowski product
Issue Date: 2019
Publisher: Soc.
Source: Electronic Journal of Linear Algebra - ELA (35): 181-186 (2019)
Journal or Series Name: The electronic journal of linear algebra 
Abstract (english): Each connected component of the Gershgorin circles of a matrix contains exactly as many eigenvalues as circles are involved. Thus, the Minkowski (set) product of all circles contains the determinant if all circles are disjoint. In [S.M. Rump. Bounds for the determinant by Gershgorin circles. Linear Algebra and its Applications, 563:215219, 2019.], it was proved that statement to be true for real matrices whose circles need not to be disjoint. Moreover, it was asked whether the statement remains true for complex matrices. This note answers that in the affrmative. As a by-product, a parameterization of the outer loop of a Cartesian oval without case distinction is derived.
ISSN: 1081-3810
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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