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

Daishi Aiura; Naonori Kakimura; Kazuo Murota

doi:10.1016/j.laa.2012.08.022

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

Daishi Aiura, Naonori Kakimura, Kazuo Murota

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1016/j.laa.2012.08.022
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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10.1016/j.laa.2012.08.022

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title = "On the number of matrices to generate a matrix * -algebra over the real field",

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.",

keywords = "Matrix * -algebra, Minimal generators, Structure theorem",

author = "Daishi Aiura and Naonori Kakimura and Kazuo Murota",

note = "Funding Information: The authors appreciate the referee for pointing to previous works on algebraic group theory and for suggesting a possible extension mentioned at the end of Section 4.3. This research is partially supported by the Aihara Project, the FIRST program from JSPS, by Global COE Program “The research and training center for new development in mathematics” from MEXT, and by Grant-in-Aid for Scientific Research.",

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AU - Murota, Kazuo

N1 - Funding Information: The authors appreciate the referee for pointing to previous works on algebraic group theory and for suggesting a possible extension mentioned at the end of Section 4.3. This research is partially supported by the Aihara Project, the FIRST program from JSPS, by Global COE Program “The research and training center for new development in mathematics” from MEXT, and by Grant-in-Aid for Scientific Research.

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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.

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KW - Minimal generators

KW - Structure theorem

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

Abstract

Keywords

ASJC Scopus subject areas

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