On the eigenvalues of the Magick Operator
Zenodo (CERN European Organization for Nuclear Research) July 25, 2023 DOI: 10.5281/zenodo.8184373 via OpenAlex
Summary
This paper explores the mathematical properties of an operator M̂, building on prior algebraic work. It focuses on events with two outcomes, labeled |1〉 and |2〉. The eigenvalue problem for M̂ⁿ is considered, and spectral decomposition yields a linear combination representation. The effect of multiple M̂ operators acting on the same state is examined, revealing that if outcomes are uncorrelated or have equal magnitude, the commutator is zero. For multiple intents, the total eigenvalue of an eigenvector equals the product of individual eigenvalues, resembling a superposition-like effect. The order of intents does not matter when generated simultaneously during a probabilistic event. Future directions include analyzing correlation coefficients, decomposing M̂ into infinitesimal operators, and studying dynamical state evolution.
Study at a glance
| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Keywords | Eigenvalues and eigenvectors Operator biology Pure mathematics Physics Genetics |
| Key finding | For multiple intents, the total eigenvalue of an eigenvector is the product of individual eigenvalues, akin to a superposition-like effect. |
Abstract
In this paper, the properties of the operator M̂ are explored, building upon the previously established algebraic foundation[1]. The focus is on events with two outcomes labelled |1〉 and |2〉. The eigenvalue problem for the operator M̂n is considered, and the operator’s action on other states is investigated. Spectral decomposition is employed, leading to a linear combination representation of the operator. The paper also examines the effect of multiple Magick operators acting on the same state. The commutation relations between these operators are analysed, revealing interesting properties. Specifically, if the outcomes are uncorrelated or have the same magnitude, the commutator is zero. The interaction between multiple intents is studied, and a fundamental result is obtained: the total eigenvalue of an eigenvector for multiple in- tents is the product of individual eigenvalues, akin to a superposition-like effect observed in nature. The order of intents is shown to be unimportant when generated simultaneously during a probabilistic event. The paper outlines future research directions, including analysing the correlation coefficient s, decomposing the operator M̂ into infinitesimal operators, and investigating the dynamical equation of state evolution under M̂ operators.