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Singular value decomposition, often abbreviated as SVD, is a fundamental matrix factorization technique in linear algebra. It decomposes any given matrix into three other matrices. For a real matrix A of size m x n, its singular value decomposition is given by A = U * Sigma * V^T, where U is an m x m orthogonal matrix, Sigma is an m x n diagonal matrix containing non-negative real numbers on its diagonal, and V^T is the transpose of an n x n orthogonal matrix V. The diagonal entries of Sigma are called the singular values of A, and they are typically arranged in descending order. The columns of U are called the left singular vectors, and the columns of V are called the right singular vectors.
Singular value decomposition has wide-ranging applications across various fields. In image processing, it is used for