4.6.1 Conceptual Foundation of Value–Price Transformation

4.6.1 Conceptual Foundation of the Price Relation Matrix

The Urban Land Value Field (ULVF) provides a theoretical representation of urban value through the Value Correlation Matrix (VCM) and the Value Relation Matrix (VRM). While these two matrices describe the intrinsic spatial organization of urban value, they do not directly represent observable land prices. Practical applications in land administration, urban planning, taxation, and compensation require a mathematical framework capable of transforming value relationships into corresponding price relationships.

To achieve this objective, the ULVF framework introduces the Price Relation Matrix (PRM). Rather than estimating the market price of each land parcel independently, the PRM preserves the relational structure established by the Urban Land Value Field and expresses it in terms of land-price relationships. Consequently, the PRM serves as the computational bridge between the theoretical value system and practical land price determination.

Unlike conventional valuation approaches that directly predict absolute land prices, the PRM maintains the spatial consistency inherited from the Value Relation Matrix. This ensures that land prices remain compatible with the underlying mechanisms governing urban value formation and spatial interaction.