SVD
Singular Value Decomposition

SVD (Singular Value Decomposition) is a critical mathematical technique in linear algebra, widely applied in AI and ML for dimensionality reduction, noise reduction, and data compression. By decomposing a matrix into three simpler matrices—U, Σ (Sigma), and V—SVD captures essential linear structures in data, making it invaluable in tasks such as Principal Component Analysis (PCA), collaborative filtering in recommendation systems, and natural language processing through Latent Semantic Analysis (LSA). Its capability to approximate datasets with fewer parameters while preserving crucial patterns and features is pivotal in enhancing computational efficiency and performance in learning algorithms.

The formal introduction of SVD traces back to the 19th century, but its application in computer science and AI became prominent in the late 20th century, particularly during the 1980s and 1990s, as computational resources and the need for efficient data processing grew.

Key contributors to the mathematical foundations of SVD include Carl Eckart and Gale Young, who formalized its foundational theories, while practical applications in AI and ML were significantly advanced by researchers employing it for text mining, image processing, and collaborative filtering.