Abstract

A permuted graph matrix is a matrix \(V \in \mathbb{C}^{(m+n)\times m}\) such that every row of the m × m identity matrix Im appears at least once as a row of V. Permuted graph matrices can be used in some contexts in place of orthogonal matrices, for instance when giving a basis for a subspace \(\mathcal{U}\subseteq \mathbb{C}^{m+n}\), or to normalize matrix pencils in a suitable sense. In these applications the permuted graph matrix can be chosen with bounded entries, which is useful for stability reasons; several algorithms can be formulated with numerical advantage with permuted graph matrices. We present the basic theory and review some applications from optimization or in control theory.

Notes

Acknowledgements

The author is grateful to C. Mehl, B. Meini and N. Strabič for their useful comments on an early version of this chapter.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly

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