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Smaller Gershgorin disks for multiple eigenvalues for complex matrices

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arxiv 2109.09000 v2 pith:K5PI6QMQ submitted 2021-09-18 math.RA math.CO

classification math.RAmath.CO
keywords matricescomplexeigenvaluesgershgorinmultiplerealalmostanother
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Extending an earlier result for real matrices we show that multiple eigenvalues of a complex matrix lie in a reduced Gershgorin disk. One consequence is a slightly better estimate in the real case. Another one is a geometric application. Further results of a similar type are given for normal and almost symmetric matrices.

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