The Matrix Theory group was created to study properties and applications of this fundamental area of mathematical knowledge. To date we have developed some work in: eigenvalue and singular value localization, linear and nonlinear preservation problems. We have also designed some applications to image processing such as: compression, resolution and edge computation of an image. We have also studied methods for the study of homologies of finite topologies via matrix representation of topologies; in this case we make use of topogeneous matrices to develop algorithms that allow us to find the core of a finite topology. Other topics that have been studied by the Matrix Theory group are associated to topics of Information Theory, in this area we have developed new linear rank inequalities on finite bodies.

• INFORMATION THEORY
• DATA ANALYSIS
• EIGENVALUE AND SINGULAR VALUE LOCALIZATION
• INFORMATION NETWORKS
• DATA

• Human and economic resources
• Transportation routes
• Food security
• Compatibilities and resources
• Robustness of communications networks and power grids
• Telecommunications
• Teletraffic
• Optimization 3.5 G