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Noncommutative Spectral Decomposition with Quasideterminant

Tatsuo Suzuki
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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.

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BibTeXRIS

Tatsuo Suzuki. 2007-03-26. Noncommutative Spectral Decomposition with Quasideterminant. https://arxiv.org/abs/math/0703751

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