English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The square root of Not is a logical operator of importance in quantumcomputing theory and of interest as a mathematical object in its own right. Inphysics, it is a square complex matrix of dimension 2. In the present work itis a complex square matrix of arbitrary dimension. The introduction of linearalgebra into logical theory has been enhanced in recent decades by theresearches in the field of neural networks and quantum computing. Here we willmake a brief description of the representation of logical operations throughmatrices and we show how general expressions for the two square roots of theNot operator are obtained. Then, we explore two topics. First, we study anextension to a non-quantum domain of a short form of Deutsch's algorithm. Then,we assume that a root of Not is a matrix extension of the imaginary unit i, andunder this idea we obtain fully matrix versions for the Euler expansions andfor the representations of circular functions by complex exponentials.

Generalized "Square roots of Not" matrices, their application to the  unveiling of hidden logical operators and to the definition of fully matrix  circular Euler functions