Component Matrices of a Square Matrix and Their Properties

Dorothea Petraki () and Nikolaos Samaras ()
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Dorothea Petraki: University of Macedonia
Nikolaos Samaras: University of Macedonia

A chapter in Mathematical Analysis, Approximation Theory and Their Applications, 2016, pp 559-572 from Springer

Abstract: Abstract The definition of the component matrices of a square matrix A is well-known [Lancaster]. This paper is concerned with all the basic properties of component matrices of a square matrix A, where A 𝜖 M ν × ν ( K ) , K = ℝ $$A\epsilon M_{\nu \times \nu }(K),K = \mathbb{R}$$ , or K = ℂ $$K = \mathbb{C}$$ . This is very useful for the studies of the spectral resolution of a matrix function f(A), the convergence of sequences and series of matrices and also the convergence of matrix functions. It is also useful to solve differential equations and control system problems.

Keywords: Component matrices; Jordan canonical form; Projection matrices; Resolvent of a matrix; Hermite interpolation; 11Cxx; 15Axx; 65H04 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-31281-1_25

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DOI: 10.1007/978-3-319-31281-1_25

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