### 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 |
---|---|

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 |

### Fingerprint

### Keywords

- Matrix * -algebra
- Minimal generators
- Structure theorem

### ASJC Scopus subject areas

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

### Cite this

*Linear Algebra and Its Applications*,

*438*(3), 1252-1266. https://doi.org/10.1016/j.laa.2012.08.022

**On the number of matrices to generate a matrix * -algebra over the real field.** / Aiura, Daishi; Kakimura, Naonori; Murota, Kazuo.

Research output: Contribution to journal › Article

*Linear Algebra and Its Applications*, vol. 438, no. 3, pp. 1252-1266. https://doi.org/10.1016/j.laa.2012.08.022

}

TY - JOUR

T1 - On the number of matrices to generate a matrix * -algebra over the real field

AU - Aiura, Daishi

AU - Kakimura, Naonori

AU - Murota, Kazuo

PY - 2013/2/1

Y1 - 2013/2/1

N2 - 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.

AB - 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.

KW - Matrix -algebra

KW - Minimal generators

KW - Structure theorem

UR - http://www.scopus.com/inward/record.url?scp=84870316371&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870316371&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2012.08.022

DO - 10.1016/j.laa.2012.08.022

M3 - Article

AN - SCOPUS:84870316371

VL - 438

SP - 1252

EP - 1266

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 3

ER -