Noncommutative Spectral Decomposition with Quasideterminant

Details Noncommutative Spectral Decomposition with Quasideterminant Noncommutative Spectral Decomposition with Quasideterminant

2007-03-26

arxiv.org/abs/math/0703751v1

Mathematics

Quantum Algebra

18 pages, no figures

Scientific paper

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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