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A matrix generalization of Euler identity e^(ix) = cosx + i sinx

Gianluca Argentini
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Abstract

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.

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BibTeXRIS

Gianluca Argentini. 2007-03-15. A matrix generalization of Euler identity e^(ix) = cosx + i sinx. https://arxiv.org/abs/math/0703448

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