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arXiv · 2011.11154

Pseudospectra and Simultaneous Power Control

Maëva Ostermann
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Abstract

We prove that, for $M>0$ and $n,m\ge2$, we can find two $10\times10$ matrices $A$ and $B$ with identical pseudospectra such that we have simultaneously $\|A^n\|/\|B^n\|>M$ and $\|A^m\|/\|B^m\|>M$. We also prove that, under certain conditions, this result holds for two more general functions of $A$ and $B$.

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Maëva Ostermann. 2020-11-23. Pseudospectra and Simultaneous Power Control. https://arxiv.org/abs/2011.11154

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