Canonical Forms and Factorizations

Larisa Beilina (), Evgenii Karchevskii and Mikhail Karchevskii
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Larisa Beilina: Chalmers University of Technology and University of Gothenburg, Department of Mathematical Sciences
Evgenii Karchevskii: Kazan Federal University, Department of Applied Mathematics
Mikhail Karchevskii: Kazan Federal University, Department of Computational Mathematics

Chapter Chapter 5 in Numerical Linear Algebra: Theory and Applications, 2017, pp 163-208 from Springer

Abstract: Abstract In this chapter we explore in detail the problem of reducing the matrix of an operator to a simple form using special bases in finite-dimensional spaces. The singular value decomposition of an operator is constructed. The Jordan canonical form of the matrix of a finite-dimensional operator is obtained. A special section is devoted to studying matrix pencils. We obtain their canonical forms and describe applications to investigate the structure of solutions of systems of ordinary linear differential equations.

Keywords: Weierstrass Canonical Form; Matrix Pencil; Pseudosolution; Singular Pencil; Cyclic Subspace (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-57304-5_5

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DOI: 10.1007/978-3-319-57304-5_5

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