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

Daishi Aiura, Naonori Kakimura, Kazuo Murota

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1252-1266
Number of pages15
JournalLinear Algebra and Its Applications
Volume438
Issue number3
DOIs
Publication statusPublished - 2013 Feb 1
Externally publishedYes

Fingerprint

Matrix Algebra
Algebra
Symmetric matrix
Genericity
Structure Theorem
Structural design
Engineering
Eigenvalue

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

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

In: Linear Algebra and Its Applications, Vol. 438, No. 3, 01.02.2013, p. 1252-1266.

Research output: Contribution to journalArticle

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