Canonical forms for Hamiltonian and symplectic matrices and pencils

Wen-Wei Lin, Volker Mehrmann*, Hongguo Xu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

86 Scopus citations


We study canonical forms for Hamiltonian and symplectic matrices or pencils under equivalence transformations which keep the class invariant. In contrast to other canonical forms our forms are as close as possible to a triangular structure in the same class. We give necessary and sufficient conditions for the existence of Hamiltonian and symplectic triangular Jordan, Kronecker and Schur forms. The presented results generalize results of Lin and Ho (On Schur type decompositions for Hamiltonian and symplectic pencils, Technical Report, Institute of Applied Mathematics, National Tsing Hua University, Taiwan, 1990) and simplify the proofs presented there.

Original languageEnglish
Pages (from-to)469-533
Number of pages65
JournalLinear Algebra and Its Applications
StatePublished - 1 Dec 1999


  • Algebraic Riccati equation
  • Eigenvalue problem
  • Hamiltonian pencil (matrix)
  • Jordan canonical form
  • Kronecker canonical form
  • Linear quadratic control
  • Symplectic pencil (matrix)

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