A matrix generalization of Euler identity e^(ix) = cosx + i sinx
经典分析与常微分方程
2007-05-23 v1 数学物理
综合数学
math.MP
流体动力学
量子物理
摘要
In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first Pauli matrix.
引用
@article{arxiv.math/0703448,
title = {A matrix generalization of Euler identity e^(ix) = cosx + i sinx},
author = {Gianluca Argentini},
journal= {arXiv preprint arXiv:math/0703448},
year = {2007}
}
备注
5 pages, research work done at R&D Dept. of Company Institution