MathematicsJanuary 20, 202624 min read

Linear Algebra Model for Negative Correlation Detection Across Business Universes

Using eigendecomposition of correlation matrices to identify conflicting objectives across business universes

When business universes optimize in opposing directions, organizations incur both direct conflict cost and wasted optimization effort. This paper develops a linear-algebra framework for detecting negative correlations using correlation matrices, eigendecomposition, and spectral analysis. Negative eigenvalues in inter-universe correlation structures identify conflict clusters that require governance intervention rather than additional local optimization.

linear-algebracorrelation-matrixeigendecompositionconflict-detectionmulti-universespectral-analysis
MathematicsDecember 28, 202544 min read

Spectral Decomposition of Conflict Clusters: Extracting Opposition Factions via Laplacian Eigenvectors

Using graph Laplacian analysis and Fiedler vectors to reveal hidden factional structure in multi-agent conflict networks

Repeated agent conflicts can form factional structures that are hard to detect from pairwise analysis alone. This paper applies spectral graph theory by constructing conflict-graph Laplacians, analyzing eigenspectra, and using the Fiedler vector to partition opposition groups. We extend to k-faction decomposition via higher eigenvectors and present visualization methods that translate spectral patterns into operational governance signals.

spectral-analysisgraph-LaplacianFiedler-vectorconflict-detectionfaction-extractionclustering