Operator Analogy of Quantum Pseudo-Logic
In this paper, we study linear operators on real and complex Euclidean spaces which are real-orthogonal projections. It is a generalization of such standard (complex) orthogonal projections for which only the real part of scalar product vanishes. We note the difference between properties of real-orthogonal projections on real and on complex spaces. We can compare some partial order properties of orthogonal and of real-orthogonal projections. We prove that the set of all real-orthogonal projections in a finite-dimensional complex or real space is a quantum pseudo-logic.
Keywords and phrasesHilbert space R-orthogonality projection partial order logic
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