Titlebook: Algorithms for Quadratic Matrix and Vector Equations; Federico Poloni Book 2011 The Editor(s) (if applicable) and The Author(s), under exc

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Linear algebra preliminariesse of . The notation I., with . often omitted when it is clear from the context, denotes the identity matrix; the zero matrix of any dimension is denoted simply by 0. With . we denote the vector of suitable dimension all of whose entries are 1. The expression ρ (.) stands for the spectral radius of the matrix .

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Constructing other matrix geometric meanse definite . × . matrices. Chapter 11 mention the desirable properties listed by Ando, Li and Mathias [6]; however, these properties do not uniquely define a multivariate matrix geometric mean; thus several different definitions appeared in literature.

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Lur’e equations of singular . has received comparatively little attention. However, the singularity of . is often a structural property of the system to be analyzed [140] and can therefore not be avoided by arguments of genericity.