On the Differential Equation of First and Second Order in the Zeon Algebra

Mansour, Toufik; Schork, Matthias

doi:10.1007/s00006-021-01126-7

Cited by 3 publications

(2 citation statements)

References 52 publications

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“…From a different perspective, differential equations of first and second order in zeon algebras have recently been studied by Mansour and Schork [7]. Combinatorial properties of zeons are prominent throughout their work.…”

Section: Introductionmentioning

confidence: 99%

A Spectral Theorem for Zeon Matrices

Staples¹

2022

Preprint

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In this paper, a spectral theorem for matrices with (complex) zeon entries is established. In particular, it is shown that when A is an m × m self-adjoint matrix whose characteristic polynomial χA(u) splits over the zeon algebra CZ n , there exist m spectrally simple eigenvalues λ1, . . . , λm and m linearly independent normalized zeon eigenvectors v1, . . . , vm such that A = m j=1 λjπj, where πj = vjvj † is a rank-one projection onto the zeon submodule span{vj} for j = 1, . . . , m.

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Section: Introductionmentioning

confidence: 99%

A Spectral Theorem for Zeon Matrices

Staples¹

2022

Preprint

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“…From a different perspective, differential equations of first and second order in zeon algebras have recently been studied by Mansour and Schork [6]. Combinatorial properties of zeons are prominent throughout their work.…”

Section: Introductionmentioning

confidence: 99%

Spectrally Simple Zeros of Zeon Polynomials

Staples

2021

Preprint

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Combinatorial properties of zeons have been applied to graph enumeration problems, graph colorings, routing problems in communication networks, partition-dependent stochastic integrals, and Boolean satisfiability. Power series of elementary zeon functions are naturally reduced to finite sums by virtue of the nilpotent properties of zeons. Further, the zeon extension of any analytic complex function has zeon polynomial representations on associated equivalence classes of zeons.In this paper, zeros of polynomials over complex zeons are considered. Existing results for real zeon polynomials are extended to the complex case and new results are established. In particular, a fundamental theorem of zeon algebra is established for spectrally simple zeros of complex zeon polynomials, and an algorithm is presented that allows one to find spectrally simple zeros when they exist. As an application, inverses of zeon extensions of analytic functions are computed using polynomial methods.

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Spectrally Simple Zeros of Zeon Polynomials

Staples

2021

Adv. Appl. Clifford Algebras

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On the Differential Equation of First and Second Order in the Zeon Algebra

Cited by 3 publications

References 52 publications

A Spectral Theorem for Zeon Matrices

A Spectral Theorem for Zeon Matrices

Spectrally Simple Zeros of Zeon Polynomials

Spectrally Simple Zeros of Zeon Polynomials

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