### Abstract

In this paper, we discuss generating a *-algebra over the real field with a set of symmetric matrices. This is motivated by an application in structural engineering. We show that any *-algebra can be generated with at most four randomly-chosen symmetric matrices. The proof relies on the structure theorem for *-algebras and the notion of genericity in eigenvalue structure.

Original language | English |
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Pages (from-to) | 1252-1266 |

Number of pages | 15 |

Journal | Linear Algebra and Its Applications |

Volume | 438 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 Feb 1 |

Externally published | Yes |

### Keywords

- Matrix * -algebra
- Minimal generators
- Structure theorem

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

Aiura, D., Kakimura, N., & Murota, K. (2013). On the number of matrices to generate a matrix * -algebra over the real field.

*Linear Algebra and Its Applications*,*438*(3), 1252-1266. https://doi.org/10.1016/j.laa.2012.08.022