Singular Value Decomposition
Singular Value Decomposition (SVD) is a mathematical technique used in linear algebra to factorize a matrix into three simpler matrices. Specifically, for any given matrix A, SVD expresses it as the product of three matrices: U, Σ, and V^T. Here, U contains the left singular vectors, Σ is a diagonal matrix with singular values, and V^T contains the right singular vectors. This decomposition helps in understanding the structure of the data represented by the matrix.
SVD is widely used in various applications, including image compression, recommendation systems, and natural language processing. By reducing the dimensionality of data, SVD can help identify patterns and relationships, making it easier to analyze large datasets. This technique is particularly valuable in machine learning and data science for improving efficiency and performance.