Permuted Graph Matrices and Their Applications

Federico Poloni ()
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Federico Poloni: Università di Pisa, Dipartimento di Informatica

Chapter Chapter 5 in Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, 2015, pp 107-129 from Springer

Abstract: 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 I m 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.

Keywords: Invariant Subspace; Negative Real Part; Full Column Rank; Algebraic Riccati Equation; Grassmann Manifold (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-15260-8_5

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