SVDs
The Singular Value Decomposition (SVD) is a fundamental factorization of a real or complex matrix. Given any matrix A, its SVD can be expressed as A = UΣV^T, where U and V are orthogonal matrices, and Σ is a diagonal matrix containing the singular values of A. The columns of U are the left singular vectors, and the columns of V are the right singular vectors. The singular values, arranged in descending order on the diagonal of Σ, represent the magnitudes of the corresponding singular vectors.
The SVD is a powerful tool with broad applications across various fields. In linear algebra, it provides