Computing \(\mu\)-values for representations of symmetric groups in engineering systems. (English) Zbl 1413.49046
Summary: In this article we consider the matrix representations of finite symmetric groups Sn over the filed of complex numbers. These groups and their representations also appear as symmetries of certain linear control systems [C. R. Danielson, Symmetric constrained optimal control. Theory, algorithms, and applications. Berkeley, CA: Berkeley, University of California (Diss.) (2014)]. We compute the structure singular values (SSV) of the matrices arising from these representations. The obtained results of SSV are compared with well-known MATLAB routine mussv.
MSC:
| 49N25 | Impulsive optimal control problems |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 20C30 | Representations of finite symmetric groups |
Keywords:
group representations; symmetric groups; \(\mu\)-values; spectral radius; family of block diagonal perturbationsReferences:
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