Mathematical foundations of linear algebra with applications to machine learning, data analysis, and computational modeling, including regression, dimensionality reduction, and network-based applications.
Focus: Linear Models · Dimensionality Reduction · Optimization · Data Analysis
Level: Undergraduate / Graduate
Connections between eigen decomposition and SVD in data analysis.
Access materialsSolving systems of linear equations and understanding solution spaces.
Access materialsIntroduction to vector spaces, basis, and geometric interpretation of linear structures.
Access materialsRepresentation of systems of equations using matrices and linear transformations.
Access materialsFundamental concepts for understanding transformations and stability in linear systems.
Access materialsClassification of systems: unique solutions, infinite solutions, and inconsistencies.
Access materialsModeling relationships between variables using linear systems and optimization.
Access materialsOptimization techniques to approximate solutions in overdetermined systems.
Access materialsStabilizing models and preventing overfitting in linear regression frameworks.
Access materialsMatrix factorization technique for dimensionality reduction and data compression.
Access materialsDimensionality reduction method widely used in machine learning and data science.
Access materialsApplication of linear algebra to ranking problems and network-based scoring systems.
Access materialsApplication of SVD to analyze ecological networks and ranking structures.
Access materialsUsing regression models to infer gene regulatory networks from biological data.
Access materialsApplication of regression techniques to analyze patterns in bioacoustic data.
Access materials