Extendable orthogonal sets of integral vectors
Fernando Chamizo, Jorge Jim\'enez Urroz
TL;DR
This paper investigates the properties of orthogonal sets of integral vectors with fixed norm, focusing on their extendability while preserving orthogonality and norm, using arithmetic properties of hypercomplex numbers.
Contribution
It introduces a novel approach leveraging quaternion and hypercomplex number properties to analyze the extendability of orthogonal integral vector sets.
Findings
Characterization of extendability conditions for orthogonal integral vectors
Use of quaternion arithmetic to analyze vector set properties
Potential applications in quantum computation models
Abstract
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the quaternions and other hypercomplex numbers.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Matrix Theory and Algorithms · Mathematical Analysis and Transform Methods