Normal matrices

Gorka Armentia; Juan-Miguel Gracia; Francisco-Enrique Velasco

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arXiv · 2106.00726

Normal matrices

Gorka Armentia·Juan-Miguel Gracia·Francisco-Enrique Velasco

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Abstract

Let $A$ be a square complex matrix and $z$ a complex number. The distance, with respect to the spectral norm, from $A$ to the set of matrices which have $z$ as an eigenvalue is less than or equal to the distance from $z$ to the spectrum of $A$. If these two distances are equal for a sufficiently large finite set of numbers $z$ which are not in the spectrum of $A$, then the matrix $A$ is normal.

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Gorka Armentia, Juan-Miguel Gracia, Francisco-Enrique Velasco. 2021-06-01. Normal matrices. https://arxiv.org/abs/2106.00726

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