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Canonical Forms of Structured Matrices and Pencils

In: Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

Author

Listed:
  • Christian Mehl

    (Technische Universität Berlin, Institut für Mathematik)

  • Hongguo Xu

    (University of Kansas, Department of Mathematics)

Abstract

This chapter provides a survey on the development of canonical forms for matrices and matrix pencils with symmetry structures and on their impact in the investigation of application problems. The survey mainly focuses on the results from three topics that have been developed during the past 15 years: structured canonical forms for Hamiltonian and related matrices, structured canonical forms for doubly structured matrices and pencils, and singular value-like decompositions for matrices associated with two sesquilinear forms.

Suggested Citation

  • Christian Mehl & Hongguo Xu, 2015. "Canonical Forms of Structured Matrices and Pencils," Springer Books, in: Peter Benner & Matthias Bollhöfer & Daniel Kressner & Christian Mehl & Tatjana Stykel (ed.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, edition 127, chapter 0, pages 131-159, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-15260-8_6
    DOI: 10.1007/978-3-319-15260-8_6
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