Positive Definiteness

Positive definiteness, a property signifying a matrix or function's ability to produce only non-negative outputs for any input vector, is crucial across diverse scientific fields. Current research focuses on ensuring and exploiting this property in various contexts, including developing algorithms that guarantee positive definiteness in model outputs (e.g., covariance functions in regression or kernels in machine learning) and employing techniques like kernel sums-of-squares and Cholesky decomposition to achieve this. This research is significant because positive definiteness is essential for ensuring the validity and interpretability of models in applications ranging from signal processing and machine learning to the modeling of physical systems.