### Abstract

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 language | English |
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Title of host publication | Applied Mathematical Sciences (Switzerland) |

Publisher | Springer |

Pages | 361-402 |

Number of pages | 42 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Publication series

Name | Applied Mathematical Sciences (Switzerland) |
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Volume | 149 |

ISSN (Print) | 0066-5452 |

ISSN (Electronic) | 2196-968X |

### Keywords

- 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