Noncommutative spectral decomposition with quasideterminant

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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

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Keywords

  • Noncommutative
  • Quasideterminant
  • Spectral decomposition

ASJC Scopus subject areas

  • Mathematics(all)

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