2018/05/08 by Arkady Bolotin, Bolotin, Arkady
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Computability, Logic, AI Algorithms #FOS: Physical sciences #Matrix Theory and Algorithms #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1805.02986
openalex publication_date 2018/05/08 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28
In contrast to conjunctions of commutable projection operators unambiguously\nrepresented by their meets, the mathematical representation of conjunctions of\nincommutable projection operators is a question that has yet to be solved. This\nquestion relates to another asking whether the set of the column spaces of the\nprojection operators, commutable and incommutable alike, forms a lattice. As it\nis demonstrated in the paper, if the Hilbert space is finite, the column spaces\nof the incommutable projection operators cannot be elements of one partially\nordered set in accordance with Burnside's theorem on matrix algebras.\n