Density Clustering Matrix: Standard Matrix as the δ-Aligned Subspace Special Case

Chao Qin

doi:10.5281/zenodo.21723563

July 31, 2026Open Access

Density Clustering Matrix: Standard Matrix as the δ-Aligned Subspace Special Case

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Key Points

This research aims to define the Density Clustering Matrix and explore its relationship to delta-aligned subspace.
Defines density clustering points as matrix elements
Uses 'Merge' for addition and 'Resonance' for multiplication
Investigates special cases in delta-aligned subspace.
Identifies standard matrix as an exact special case of the Density Clustering Matrix
Demonstrates interactions between density clusterings and matrix operations.

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Implication

Defines the Density Clustering Matrix properties in mathematics, showing its special case in delta-aligned subspace.

Abstract

Field Domain Mathematics posits that numbers are density clusterings in space. This paper defines the Density Clustering Matrix with elements as density clustering points, addition as Merge and multiplication as Resonance. Key finding: standard matrix is an exact special case on the delta-aligned subspace.

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Chao Qin (2026) studied this question.

synapsesocial.com/papers/6a6eeb011b0468a7eeab3c0b https://doi.org/10.5281/zenodo.21723563

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Density Clustering Matrix: Standard Matrix as the δ-Aligned Subspace Special Case

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Density Clustering Matrix: Standard Matrix as the δ-Aligned Subspace Special Case

Key Points

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Implication

Abstract

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