Paper Details

Name: Shashikumar R
Country: India

Year: 2025
Volume: Volume-12, Issue-1 (January-June)
Page Number: 284-304
DOI: https://doi.org/10.5281/zenodo.23031126

Linear algebra has evolved from a foundational mathematical discipline concerned with vectors, matrices, transformations, and systems of equations into a computational language underlying modern analytics, optimization, network science, artificial intelligence, and decision support. Despite this extensive diffusion, research concerning matrix-based modelling remains fragmented across mathematics, computer science, operations research, engineering, information systems, and management. This systematic review develops an integrated perspective on how matrix representations and transformations have progressed from mathematical computation toward complex-system modelling and managerial decision intelligence. The review synthesizes literature around five interconnected domains: mathematical representation, matrix transformation, complex-system modelling, optimization and decision analysis, and management analytics. Particular attention is given to matrix decomposition, eigenvalue methods, singular value decomposition, principal component analysis, adjacency and transition matrices, multi-criteria decision-making, optimization, machine learning, and business analytics. PRISMA 2020 is adopted as the reporting framework, while bibliometric and thematic techniques are proposed for mapping the intellectual structure of the field. The synthesis indicates that matrices increasingly function not merely as computational objects but as representational infrastructures through which heterogeneous organizational data, relationships, dependencies, alternatives, and constraints can be transformed into decision-relevant structures. The review further develops a Matrix-to-Decision Intelligence (MDI) framework comprising four stages: representation, transformation, optimization, and decision intelligence. The framework positions linear algebra as a connective layer between data and managerial action and identifies emerging research opportunities around explainable matrix models, dynamic and high-dimensional systems, hybrid matrix-AI architectures, uncertainty-aware decision models, and human-centred decision intelligence. The study contributes a cross-disciplinary conceptual architecture for researchers seeking to connect mathematical modelling with contemporary management analytics.

Keywords: linear algebra; matrix-based models; decision intelligence; complex systems; management analytics; optimization; network science; machine learning; systematic review; bibliometric analysis