Singulärvärdesuppdelning

Singulärvärdesuppdelning, also known as singular value decomposition (SVD), is a matrix factorization technique used in linear algebra and numerical analysis. It decomposes a given matrix into three other matrices, providing a way to understand the structure and properties of the original matrix. The SVD of a matrix A is given by the equation A = UΣV*, where U and V are orthogonal matrices, and Σ is a diagonal matrix containing the singular values of A. The columns of U and V are called the left and right singular vectors, respectively. The singular values in Σ are the square roots of the eigenvalues of A*A and A*A, and they represent the strength of the corresponding singular vectors. SVD has numerous applications in various fields, including data compression, image processing, and machine learning. It is particularly useful for solving linear systems, computing matrix inverses, and finding the best low-rank approximation of a matrix. The SVD is a powerful tool for analyzing and manipulating matrices, providing insights into their underlying structure and properties.