Efficient transformation for block-diagonalization

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter


Use of block-diagonalization of the Jacobian matrix in bifurcation analysis of symmetric systems was demonstrated in Chap. 12. By taking advantage of the underlying geometrical structure of dihedral group symmetry, we give a systematic procedure to determine the transformation matrix for block-diagonalization and an efficient method to compute the block-diagonal form. Group representation theory in Chap. 7, theory of block-diagonalization in Chap. 8, and the application of these theories to the dihedral group in Chap. 9 form a foundation of this chapter.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
Number of pages42
Publication statusPublished - 2019 Jan 1

Publication series

NameApplied Mathematical Sciences (Switzerland)
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X


  • Block-diagonalization
  • Computational efficiency
  • Dihedral group
  • Jacobian matrix
  • Orbit
  • Symmetry
  • Transformation matrix
  • Truss structure

ASJC Scopus subject areas

  • Applied Mathematics

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  • Cite this

    Ikeda, K., & Murota, K. (2019). Efficient transformation for block-diagonalization. In Applied Mathematical Sciences (Switzerland) (pp. 361-402). (Applied Mathematical Sciences (Switzerland); Vol. 149). Springer. https://doi.org/10.1007/978-3-030-21473-9_13