Linear Dependence

Linear dependence, the extent to which variables or functions are related, is a central concept across diverse scientific fields, with research focusing on identifying and quantifying these relationships, particularly in complex systems. Current efforts involve developing robust methods for detecting linear dependence, even in the presence of noise or nonlinear interactions, often employing techniques from linear algebra, machine learning (e.g., neural networks, Gaussian processes), and information theory (e.g., mutual information). Understanding and managing linear dependence is crucial for improving model accuracy, interpretability, and efficiency in applications ranging from neural network design and control systems to statistical analysis and anomaly detection.