Linear Algebra in Predictive Conflict Analysis: Mathematical Frameworks for Forecasting and Mitigation

This paper creates an analytical approach to model conflict behaviors and network patterns and financial networks in interconnected systems. The proposed method combines Markov transition matrices which model probabilistic state shifts with subspace decomposition methods for networked data analysis that uses null space and singular values and LU factorization for following critical paths in transactional matrices. The proposed framework shows its effectiveness when implementing it to simulated conflict scenarios through which mathematical abstractions reveal system weaknesses to guide disruption planning.