2007/03/26 by Tatsuo Suzuki, Suzuki, Tatsuo
Physics and Astronomy · Mathematics · #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.math/0703751
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.