Products of projections and self-adjoint operators

Arias, María Laura; Gonzalez, M. Celeste

doi:10.1016/j.laa.2018.05.036

Cited by 3 publications

(1 citation statement)

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“…Furthermore, because each projection that used in this article is an orthogonal projection, the term will be simplified to just a projection. Theorem 1.1 [10] An operator 𝑃 on a Hilbert space ℋ is a projection on 𝑀 subspaces of ℋ if and only if…”

Section: Introductionmentioning

confidence: 99%

Characterization of Directed Graphs Representing C*-Algebra of Complex Matrices

Hidayat,

Herlinawati

2024

E3S Web Conf.

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Quantum mechanics is a study that plays a major role in determining the biological intelligence of Artificial Intelligence (AI). Point particle systems in quantum mechanics can be explained using C*-Algebra which is called CAR-algebra. There is a special case in the CAR-algebra which is isomorphic to the C*-algebra of complex matrices. On the other hand, C*-algebras of direct sum of complex matrix spaces is isomorphic to C*-algebra constructed by orthogonal projection and partial isometries operators via the Cuntz-Krieger relations of a directed graph. This article will provide a basis for the relationship between quantum mechanics and graphs through a discussion of the characterization of graphs that can represent C*-algebra of complex matrices. It is found that C*-algebra complex matrices n × n is a directed graph without cycles with n – 1 arrows, a single source, and has n path from the source.

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Section: Introductionmentioning

confidence: 99%