A Gentle Introduction to Singular-Value Decomposition for Machine Learning - Machine Learning Mastery

The diagonal values in the Sigma matrix are known as the singular values of the original matrix A. The columns of the U matrix are called the left-singular vectors of A, and the columns of V are called the right-singular vectors of A. The SVD is calculated via iterative numerical methods. We will not go into the details of these methods. Every rectangular matrix has a singular value decomposition, although the resulting matrices may contain complex numbers and the limitations of floating point arithmetic may cause some matrices to fail to decompose neatly. The singular value decomposition (SVD) provides another way to factorize a matrix, into singular vectors and singular values. The SVD allows us to discover some of the same kind of information as the eigendecomposition. However, the SVD is more generally applicable.