Boundary Metric from Projection-Induced Finite Rank
Pasquale Camelia
Abstract
This work investigates the notion of metric induced by finite-rank projection.Assuming a non-isometric projection with finite effective rank, the paper showsthat a unique operational boundary metric emerges as a criterion ofdistinguishability, determined by the truncated singular value decomposition.This is a preliminary, pre-review version made publicly available on Zenodo.
Topics & Concepts
MathematicsMetric (unit)Projection (relational algebra)Boundary (topology)Rank (graph theory)Boundary value problemMathematical analysisWork (physics)Discrete mathematicsPure mathematicsFisher information metricFinite setMetric spaceSingular valueIntrinsic metricCombinatoricsMatrix Theory and AlgorithmsMathematical and Theoretical AnalysisStatistical Mechanics and Entropy