The construction of maximum independent set of matrices via Clifford algebras

DEĞİRMENCİ N., ÖZDEMİR N.

TURKISH JOURNAL OF MATHEMATICS, vol.31, no.2, pp.193-205, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 2
  • Publication Date: 2007
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.193-205
  • Keywords: Hurwitz theorem, Clifford algebras, maximum independent set of matrices, REAL LINEAR COMBINATIONS
  • Anadolu University Affiliated: Yes

Abstract

In [1], [2] and [6] the maximum number of some special type n x n matrices with elements in F whose nontrivial linear combinations with real coefficients are nonsingular is studied where F is the real field R, the complex field C or the skew field H of quaternions. In this work we construct such matrices explicitly by using representations of Clifford algebras. At the end we give some analogues of the celebrated theorem of Radon-Hurwitz.