Multi-companion matrices

Boshnakov, Georgi N. (2002) Multi-companion matrices. Linear Algebra and its Applications, 354 (1-3). p. 53. ISSN 0024-3795

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Abstract

In this paper, we introduce and study the class of multi-companion matrices. They generalize companion matrices in various ways and possess a number of interesting properties. We find explicit expressions for the generalized eigenvectors of multi-companion matrices such that each generalized eigenvector depends on the corresponding eigenvalue and a number of quantities which are functionally independent of the eigenvalues of the matrix and (up to a uniqueness constraint) of each other. Moreover, we obtain a parameterization of a multi-companion matrix through the eigenvalues and these additional quantities. The number of parameters in this parameterization is equal to the number of non-trivial elements of the multi-companion matrix. The results can be applied to statistical estimation, simulation and theoretical studies of periodically correlated and multivariate time series in both discrete- and continuous-time.

Item Type: Article
Uncontrolled Keywords: Jordan decomposition; Continuous-time autoregression; Generalized eigenvectors
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
MSC 2010, the AMS's Mathematics Subject Classification > 62 Statistics
Depositing User: Ms Lucy van Russelt
Date Deposited: 20 Jul 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/402

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