On the eigenvalues of the Magick Operator

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.