Noncommutative spectral decomposition with quasideterminant

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative Cayley-Hamilton's theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it has noncommutative entries. As examples, the noncommutative spectral decomposition and the exponential matrices of a quaternionic matrix and of a matrix with entries being harmonic oscillators are given.

Original languageEnglish
Pages (from-to)2141-2158
Number of pages18
JournalAdvances in Mathematics
Volume217
Issue number5
DOIs
Publication statusPublished - 2008 Mar 20
Externally publishedYes

Keywords

  • Noncommutative
  • Quasideterminant
  • Spectral decomposition

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Noncommutative spectral decomposition with quasideterminant. / Suzuki, Tatsuo.

In: Advances in Mathematics, Vol. 217, No. 5, 20.03.2008, p. 2141-2158.

Research output: Contribution to journalArticle

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AB - We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative Cayley-Hamilton's theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it has noncommutative entries. As examples, the noncommutative spectral decomposition and the exponential matrices of a quaternionic matrix and of a matrix with entries being harmonic oscillators are given.

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