Bünger, Florian; Rump, Siegfried M. The determinant of a complex matrix and Gershgorin circles. (English) Zbl 1430.15006 Electron. J. Linear Algebra 35, 181-186 (2019). The authors prove that for a complex matrix the set product of Gershgorin circles contains the determinant. This statement has been previously shown for real matrices. Reviewer: Natalia Bebiano (Coimbra) Cited in 1 ReviewCited in 2 Documents MSC: 15A15 Determinants, permanents, traces, other special matrix functions 15A42 Inequalities involving eigenvalues and eigenvectors 51A20 Configuration theorems in linear incidence geometry Keywords:Gershgorin circle; determinant; Minkowski product PDFBibTeX XMLCite \textit{F. Bünger} and \textit{S. M. Rump}, Electron. J. Linear Algebra 35, 181--186 (2019; Zbl 1430.15006) Full Text: DOI References: [1] R.T. Farouki, H.P. Moon, and B. Ravani. Minkowski geometric algebra of complex sets. Geometriae Dedicata, 85:283- 315, 2001. · Zbl 0987.51012 [2] R.T. Farouki and H. Pottmann. Exact Minkowski products of N complex disks. Reliable Computing, 8:43-66, 2002. · Zbl 1028.65048 [3] S.M. Rump. Bounds for the determinant by Gershgorin circles. Linear Algebra and its Applications, 563:215-219, 2019. · Zbl 1405.15011 [4] H. Schneider. An inequality for latent roots of a matrix applied to determinants with dominant main diagonal. Journal of the London Mathematical Society, 28:8-20, 1953. · Zbl 0050.01103 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.