تقرير
Joint spectral radius and forbidden products
| العنوان: | Joint spectral radius and forbidden products |
|---|---|
| المؤلفون: | Vladimirov, Alexander |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control |
| الوصف: | We address the problem of finite products that attain the joint spectral radius of a finite number of square matrices. Up to date the problem of existence of "forbidden products" remained open. We prove that the product $AABABABB$ (together with its circular shifts and their mirror images) never delivers the strict maximum to the joint spectral radius if we restrict consideration to pairs $\{A,B\}$ of real $2\by 2$ matrices. Under this restriction circular shifts and their mirror images constitute the class of isospectral products and hence they all have the same spectral radius for any pair $\{A,B\}$ of $2\by 2$ matrices, even complex. For pairs of complex matrices we have numerical evidence that $AABABABB$ is still a fobidden product. A couple of binary words that encode products from this isospectral class also happen to be the shortest forbidden patterns in the parametric family of double rotations. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.17524 |
| رقم الأكسشن: | edsarx.2406.17524 |
| قاعدة البيانات: | arXiv |
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