Noncommutative spectral decomposition with quasideterminant

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)2141-2158
ページ数18
ジャーナルAdvances in Mathematics
217
5
DOI
出版ステータスPublished - 2008 3 20
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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